### 1 

### MEMORANDUM

To: Timothy Leighton, EPA; Bob Ross, Summ itec Inc.; Andrew Yin, Summitec Inc.
From: Jonathan Cohen, ICF International, Inc.
Date: October 3, 2012

Re: Contract No.: EP-W-11-014 TAF 1-6-3: Liquid Pour AEATF Study Sta tistical Review for HSRB

Introduction and Summary In August 2012, AEATF submitted the final report for their study “A Study for Measurement of Potential Dermal and Inhalation Exposure during Application of a Liquid Antimic robial Pesticide Product Du ring Manual Pouring of a Liquid Containing an AntiMicrobial.” ICF International, Inc. (ICF) was asked by EPA through Summitec Inc. to analyze the data from this study to investigate the relationshi p between dermal and inhalation exposures and the pesticide product usage. Note that much of the SAS code us ed for these analyses and some of the following description was adapted from Sarkar’s SAS code (which, in turn, was based on code provided by the AHETF) and his June 2010 Statistical Review “Review of Sta tistical Analyses in Agricultural Handler Exposure Task Force (AHETF) Monographs.”
The study report describes the experiment al study methodology and the measuremen ts in detail. Briefly, the study was carried out at an indoor test site in Concord, Ohio. Each of 18 volunteer subjects performe d both the following scripted Conventional Pour study and the following scripted Reduced Splash, in a randomly selected order.
For the Conventional Pour (CP) study, 18 volunteer subjects, referred to here as “workers,” were randomly assigned into three groups of six subjects, num bered 1, 2 and 3, and the workers in gr oup 1 were randomly assigned into two groups of three subjects, refe rred to as groups 1a and 1b. The workers in group 1a were assigned a task of pouring a liquid containing the active i ngredient DDAC from a set of 10 conventional small source containers of sizes 24, 32, and 64 fl oz into 32 fl oz trigger spray bo ttles. The workers in group 1b were assi gned a task of pouring a liquid containing the active ingredient DDAC from a set of 10 conventional small source containers of sizes 24, 32, and 64 fl oz into 2 gallon buckets. The workers in group 2 were assigned a task of pouring a liquid cont aining the active ingredient DDAC from a set of 10 conventional medi um source containers of sizes 128, 202, and 256 fl oz into either 2 gallon buckets, 4 gallon buckets, or 50 gallon low-walled troughs, where the three receiver container types were each randomly assigned to two of the group 1 workers. The work ers in group 3 were assigned a task of pouring a liquid containing the active ingredient DDAC from a set of conventi onal large source containers of sizes 640 fl oz (5 gallon buckets) with standard flat lids into 50 gallon low-walle d troughs. All subjects in grou p 1 and 4 randomly selected subjects in group 2 used a measuring cup. For each subject in groups 1 and 2, it was randomly determined whether the receiving containers would be placed on the floor or on a table (at waist to ches t height). For all subjects in group 3, the receiving containe rs were on the floor.

### 2 

### For the Reduced Splash (RS) study, the same 18 volunteer su bjects, referred to here as “workers,” were randomly assigned into three groups of six subjects, numbered 1, 2 and 3, and the workers in gr oup 1 were randomly assigned into two groups of three s ubjects, referred to as groups 1a and 1b. All these assignments were independent of the Conventional Pour study assignments, so that a worker might not be in the same groups for the CP and RS studies. The workers in group 1a were assigned a task of pouring a liquid containing th e active ingredient C14 ADBAC from a set of 10 reduced splash small source containers of size 64 fl oz into 32 fl oz trigger spray bottles. The workers in group 1b were assigned a task of pouring a li quid containing the active ingredient C14 ADBAC from a set of 10 reduced splash small source containers of size 64 fl oz into 2 gall on buckets. The workers in gr oup 2 were assigned a task of pouring a liquid containing the active i ngredient C14 ADBAC from a set of 10 reduced splash medium source containers of sizes 96, 128 and 180 fl oz into either 2 gallon buckets, 4 gall on buckets, or 50 gall on low-walled troughs, where the three receiver container types were each randomly assigned to two of the group 1 workers. The workers in group 3 were assigned a task of pouring a liquid containing the active ingredie nt C14 ADBAC from a set of large source containers of sizes 640 fl oz (5 gallon buckets) that had lids with a pull- out pour spout into 50 gallon low-walled troughs. All subjects in group 1, and 4 random ly selected subjects in group 2, used a measuring cup. For each subject in groups 1 and 2, it was randomly determined whether the receivi ng containers would be placed on the floor or on a table (at waist to chest height). For all subjects in gr oup 3, the receiving contai ners were on the floor.
Each subject was given inner and outer dosimeters to wear and was also given a personal air-sampling pump attached to an OVS air sampling tube. The air sampling pump was switched on at the beginning of the first monitoring experiment (ME) and turned off once the pouring was comp leted. The subject sat on a ch air covered with plastic sheeting until the preparation of the containers for the second ME wa s completed. Then the air sampling pump was switched on again for the second ME and turned off once the pouring was completed. The air sampling tubes, hand wash, face/neck wipes, outer dosimeters, and inner dosimeters, were collected by a researcher and were later analyzed by the laboratory to measure the mass of DDAC (attributable to the Conventional Pour active ingredient) and the mass of C14 ADBAC (attributab le to the Reduced Splash active ingredient).
The exposure measurements in the report were corrected for the average percentage recove ry of field fortification samples and for the removal efficiency of hand wash (90 %) and face and neck (89%) wipe samples. These analyses used the corrected measurements. An Excel spreadsheet containing the data in the report was supplied by the Study Director and used for these analyses. This included the uni ts conversion of the amounts of active ingredient from mg into pounds and of the mass from μg to mg. The report da ta for inhalation exposure we re unchanged other than the units conversions and some corrections to the tabulated air sampling durations in the original stud y report that were noted by the Study Director in September 2012. The derm al exposure data were us ed to develop exposure measurements for four dermal exposure routes, as follows:

• Long Dermal . This case represents the dermal exposure fo r a subject wearing long pants and long-sleeved shirts, without gloves. The exposure is the sum of the mass from hand wash, face and neck, and the six inner dosimeters (lower arm, upper arm, lower leg, upper leg, front torso, rear torso).

• Short Dermal . This case represents the dermal exposure for a subject wearing short pants and short-sleeved shirts, without gloves. The exposure is the sum of the mass from hand wash, face and neck, the outer dosimeters for the lower arm and lower leg, and the six inner dosimet ers (lower arm, upper arm, lower leg, upper leg, front torso, rear torso).

• Long Short Dermal . This case represents the dermal exposure for a subject wearing long pants and shortsleeved shirts, without gloves. The ex posure is the sum of the mass from hand wash, face and neck, the outer dosimeter for the lower arm, and the six inner dosimet ers (lower arm, upper arm, lower leg, upper leg, front torso, rear torso).

### 3 

### • Hands Only . This case represents the dermal exposure to the hands only and is the mass from hand wash. This case is used for comparison purposes. The report only considered the dermal exposure for the “Long Dermal” case, and used the same definition. However for our analyses we chose a more consistent, and more conserva tive (i.e., more health protec tive) approach to deal with values reported as being below th e level of quantitation (LOQ):

Several of the measured values were below the level of quantitation (LOQ). Su ch values are called “non-detects.” The experimental protocol also required that measurements of the inner dosimeters were not taken if the outer dosimeter was below the LOQ, although this did not in fact apply for an y of the outer dosimeter measurements made in this study. As a slightly more conservati ve (i.e., more health protective) approach th an the method used in the report, we replaced any value that was either a non-detect or was not measured by one half the LOQ. If any inner or outer dosimeter value was below the LOQ, 3 μg, each such value was replaced by 1.5 μg = 0.0015 mg. For example, if all the inner dosimeters were below the LOQ, then the total would be replaced by 0.009 mg. If the face and neck measurement was below the LOQ, 50 ng, it was replaced by 25 ng = 0.000025 mg. If the inhalation mass OVS measurement (mg) was below the LOQ, 10 ng, it was replaced by 5 ng = 0.000005 mg. All the hand wash measurements in the study were above the LOQ. For the Conventional Pour, 4 of the 18 f ace and neck measurements, 67 of the 108 outer dosimeter measurements, 107 of the 108 inner dosimeter measuremen ts, and 6 of the 18 OVS meas urements were below the LOQ. For the Reduced Splash, 0 of the 18 face and neck me asurements, 41 of the 108 outer dosimeter measurements, 105 of the 108 inner dosimeter measurements, and 9 of the 18 OVS measurements were below the LOQ. In Tables 10 and 11 below, we present the results of alternative analyses of values below th e LOQ that demonstrate that the impact of the method for analyzing non- detect samples is negligible. For three subjects and MEs (Re duced Splash ME 1 in group 1a, Reduced Splash ME 7 in group 2, and Conventional Pour ME 6 in group 1b), the hand exposure measurements were much higher than values for all other subjects in the same group. The liquid pour scenario is one in which unusually large hand exposur es can occur through random dripping and spilling events that may be poorly associated with the total amount of active ingredient used. No adjustments were made in these analyses for these potential outliers. In Table 10 below, we analyze the impact of removing these outliers. Inhalation exposure was measured usi ng the air sampling OVS tubes. The i nhalation exposure co ncentration (mg/m 3 

### ) was calculated by dividing the corr ected residue mass by the volume of air drawn. The following exposure concentrations are analy zed in this memorandum:

• Inhalation Concentration (mg/m 3 

### ). Concentration measured by the OVS tube.

• Inhalation Dose (mg). Inhalation Concentration (mg/m 3 

### ) × Air Sampling Duration (hr) × Breathing Rate for Light Activity (m 3 

### /hr). A breathing rate of 1 m 3 

### /hr is assumed.

• 8-Hour Time Weighted Average (TWA) Concentration (mg/m 3 

### ). Average concentration over eight hours that includes this period of liquid pouring activity. Inhalation Concentration (mg/m 3 

### ) × Air Sampling Duration (hr) / 8 (hr). In this memorandum we present the analysis of the unit or normalized exposure defined as the dermal or inhalation exposure divided by the pounds of active i ngredient handled. Estimates of the arithmetic and geometric means and standard deviation as well as the 95 th 

### percentile are computed using the empiri cal data for each group as well as two statistical models: the lognor mal simple random sampling model for each group and the lognormal mixed model with groups. Because the study design used predetermined groups of containers, these analyses take into account the possibility that the mean exposure depends upon the group, whic h in statistical terminology represents a fixed effect rather than a random effect. Unlike the pr eviously analyzed mop, wipe, and aerosol studies, this st udy does not have a

### 4 

### random cluster effect and so the statistical models used here are very different. The empirica l model calculates statistics for all the unit exposure measurements on a group of subject s assuming the data are statis tically independent with a possibly different distribution for each group. The lognormal si mple random sampling model cal culates statistics for all the unit exposure measurements on a group of subjects a ssuming the unit exposure measur ements are statistically independent with a lognormal distribution that can be di fferent for each group. The lognormal mixed model is fitted to the entire set of 36 exposure measurements, from both studi es, and assumes that the loga rithm of the exposure has a normal distribution with a mean that va ries between groups, a random worker effe ct, and a residual error. The random worker effect is a random value associat ed with each of the 18 workers that repr esents the possibility of clustering or association between the two measuremen ts made for that worker (one for conventional pour and one for reduced splash), expressing the possibility that some workers have a tendency for getti ng more highly exposed to antimicrobials than other workers. Although the experimental design randomized for the effects of whether a meas uring cup was used and whether the receiving container was placed on the floor or on a table, we treated these effect s as part of the random error and did not directly include those effects in th e statistical models. However, in many cas es we found a strong worker effect, and so this effect is specifically included in the mixed model so that correlations between consecutive measurements on the same worker (e.g., for the conventional pour and redu ced splash MEs) can be adjusted for.
As discussed below, we considered vari ous groupings. Initially we separately considered the six groups of container sizes 1, 2 and 3 separately for CP and RS. Since groups 1a and 1b represent very different scenarios of pouring into trigger sprays versus pouring into a larger container, with much higher observed exposures for trigger sprays due to the more complex nature of that task, we also considered separating group 1 into groups 1a and 1b. We also considered combining the data for the CP and RS for each of these c ontainer size groups. For the fi nal lognormal mixed model we used three groups: 1a with CP and RS combined; 1b, 2 a nd 3 for CP only, and 1b, 2 and 3 for RS only. Separation of the 1a group is justified due to the large difference between scenarios of pouring into larger containers and scenarios of pouring into small trigger spray bottles. For the pouring into trigger spray bottles, the CP and RS unit exposure values were not statistically signif icantly different and so coul d be combined. Although the remaining groups 1b, 2 and 3 have large differences in unit exposure, it is appropriate to combine these data into a single group of container sizes because of the difficulties in creating different regulations for pouring liquids from cont ainers of different sizes. However for the pouring into non-trigger spray bottles, the unit exposure values were significan tly different between CP and RS and so those scenarios were also separated. In summa ry we present results for the following groupings: Initial groupings:

• 1aCP. Pouring from small conventional pour containers into tr igger spray bottles

• 1aRS. Pouring from small reduced splash containers into trigger spray bottles

• 1a. Pouring from small containe rs into trigger spray bottles

• 1bCP. Pouring from small conventional pour containers not into trigger spray bottles

• 1bRS. Pouring from small reduced splash containers not into trigger spray bottles

• 1b. Pouring from small containers not into trigger spray bottles

• 2CP. Pouring from medium conventional pour containers

• 2RS. Pouring from medium reduced splash containers

• 2. Pouring from medium containers

### 5 

### • 3CP. Pouring from large conventional pour containers

• 3RS. Pouring from large reduced splash containers

• 3. Pouring from large containers Final groupings used in lognormal mixed model:

• Bottle. Pouring from CP and RS cont ainers into trigger spray bottles

• Conventional. Pouring from conventional cont ainers not into trigger spray bottles

• Reduced Splash. Pouring from reduced splash containers not into trigger spray bottles For each summary statistic we present confidence intervals. We also compute the fold relative accuracy of the summary statistics and compare with the study design benchmark of 3-fold accuracy, which was me t for the mixed model used for the main statistical analyses for all the dermal and i nhalation exposures except for dermal exposures in the Bottle grouping. To evaluate the statis tical models we present qu antile-quantile plots to co mpare the fit of normal and lognormal distributions to the data. The statistical models for the normalized exposure assume that the mean value of the logari thm of the exposure is equal to an intercept plus the slope times the logarithm of the am ount of active ingredient use d, where the slope equals 1. To test this “log-log-linearity” assumption, th e mixed model with a slope term was f itted to the data and a 95% confidence interval for the slope was calculated. A statistical test wa s used to determine if the slope was 1 or 0, corresponding either to a valid normalized exposure model or to a case where the exposure is independe nt of the amount of active ingredient used. We applied this test to the three dermal exposures a nd to the three inhalati on exposures using the statistical mixed model. For dermal exposures it is reas onable to assume on physical grounds that the same patterns ought to apply to any type of dermal expos ure, so that the slope should either be one for all types of dermal exposure or not one for all types of dermal exposure. To evaluate this issue we applied the same log-log-linearity test to a hypothetical all dermal exposure case repr esenting a janitor with no clothing, usi ng a dermal exposure estimated as the sum of the exposures measured on the face and neck, hands, a nd all the inner and outer dosimeters. We also developed a statistical repeated measures model to analyze the three main types of dermal exposure (excluding hands only) in a single statistical model, accounting for w ithin-worker correlations a nd within-location clusteri ng. We also evaluated quadratic regression models. The results for all the dermal concentration exposure routes show that the estimated in tra-cluster correlation (ICC) coefficient for the worker effect is between 0.2 and 0.4, which im plies that there are some work er effects, and therefore, in particular, differences between exposu res for different workers, as might be expected. The results for the inhalation exposures show an ICC of zer o, showing no worker effects. The mixed model results for the four dermal exposure rout es show small positive or negative slopes of between -0.3 and 0.2. These dermal exposure models consistently reject log- log-linearity (slope equals one) at the 5% significance level. These dermal exposure models also consistently do not reject independence (slope equals zero) at the 5% significance level. The finding that the de rmal exposure could be independent of the amount of active ingredient may be due to the fact that the dermal exposure is primarily cau sed by accidental splashes and spills which may be related to the shape and volume of the source cont ainer but otherwise not very strongly to the volume poured. The experimental design did not allow the concentrations to be varied within th e Conventional or Reduced Splash experiments since using much higher concentrations would require the need for prot ective gloves. For this s cenario a stronger log-loglinearity between exposure and concentration can be e xpected than between exposure and volume poured. For the inhalation exposures, the estimated slopes are close to one , log-log-linearity is not re jected, and independence is rejected.

### 6 

### Summary statistics of exposure per po unds of active ingredient handled

Tables 1 to 7 summarize the normalized e xposure data (per lb active ingredient handled) with the summary statistics from the 18 measurements for each dermal and inhalation ex posure route, for the various container groups described above. These analyses assume that the exposure measur ements within each group come from some unspecified distribution for that group. Table 1. Summary statistics for normalized long dermal exposure (mg/lb AI) using empirical sampling model.

Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent ional Reduced Splash

Arithmetic Mean 155 111 200 11 20 3 7 7 7 2 4 0 155 8 4

Arithmetic Standard Deviation 152 14 227 13 14 3 9 6 12 4 5 0 152 9 8

Geometric Mean 116 110 123 6 17 2 4 4 4 1 2 0 116 4 1

Geometric Standard Deviation 2 1 3 4 2 3 4 5 3 4 3 2 2 4 4

Min 40 95 40 1 10 1 0 0 1 0 1 0 40 0 0

5% 40 95 40 1 10 1 0 0 1 0 1 0 40 0 0

10% 40 95 40 1 10 1 1 0 1 0 1 0 40 1 0

25% 95 95 40 1 10 1 2 2 2 0 1 0 95 1 0

50% 107 115 99 8 14 1 4 7 3 1 1 0 107 6 1

75% 122 122 459 14 35 7 10 14 4 1 4 1 122 14 3

90% 459 122 459 35 35 7 15 15 31 4 14 1 459 15 7

95% 459 122 459 35 35 7 31 15 31 14 14 1 459 35 31

Max 459 122 459 35 35 7 31 15 31 14 14 1 459 35 31



### Table 2. Summary statistics for normalized short dermal exposure (mg/lb AI) using empirical sampling model.

Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent ional Reduced Splash

Arithmetic Mean 158 114 202 13 22 3 8 8 8 3 4 1 158 9 4

Arithmetic Standard Deviation 153 11 229 14 16 3 9 6 12 4 6 1 153 10 8

Geometric Mean 119 113 124 7 18 3 4 5 4 1 2 1 119 5 2

Geometric Standard Deviation 2 1 3 3 2 2 3 4 3 3 3 2 2 4 3

### 7 Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent ional Reduced Splash

Min 41 102 41 2 11 2 1 1 1 0 1 0 41 1 0

5% 41 102 41 2 11 2 1 1 1 0 1 0 41 1 0

10% 41 102 41 2 11 2 1 1 1 1 1 0 41 1 1

25% 100 102 41 2 11 2 2 2 2 1 1 1 100 1 1

50% 109 116 100 9 14 2 4 7 4 1 2 1 109 6 2

75% 123 123 465 14 40 7 11 14 4 2 4 1 123 14 4

90% 465 123 465 40 40 7 15 15 32 4 16 2 465 16 7

95% 465 123 465 40 40 7 32 15 32 16 16 2 465 40 32

Max 465 123 465 40 40 7 32 15 32 16 16 2 465 40 32



### Table 3. Summary statistics for normalized long short derm al exposure (mg/lb AI) using empirical sampling model.

Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent ional Reduced Splash

Arithmetic Mean 156 111 201 11 20 3 8 8 7 2 4 0 156 8 4

Arithmetic Standard Deviation 152 14 228 13 13 3 9 6 12 4 5 0 152 9 8

Geometric Mean 117 110 123 6 17 2 4 5 4 1 2 0 117 4 1

Geometric Standard Deviation 2 1 3 4 2 2 3 4 3 4 3 2 2 4 4

Min 41 95 41 1 10 1 1 1 1 0 1 0 41 1 0

5% 41 95 41 1 10 1 1 1 1 0 1 0 41 1 0

10% 41 95 41 1 10 1 1 1 1 0 1 0 41 1 0

25% 95 95 41 2 10 1 2 2 2 0 1 0 95 1 0

50% 108 116 100 8 14 2 4 7 3 1 1 0 108 6 1

75% 123 123 461 14 35 7 11 14 4 1 4 1 123 14 3

90% 461 123 461 35 35 7 15 15 31 4 14 1 461 15 7

95% 461 123 461 35 35 7 31 15 31 14 14 1 461 35 31

Max 461 123 461 35 35 7 31 15 31 14 14 1 461 35 31



### Table 4. Summary statistics for normalized hands only derm al exposure (mg/lb AI) using empirical sampling model.

### 8 Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent ional Reduced Splash

Arithmetic Mean 153 109 197 11 20 3 7 7 7 2 4 0 153 8 4

Arithmetic Standard Deviation 152 14 227 13 14 3 9 6 12 4 5 0 152 9 8

Geometric Mean 114 108 119 6 17 2 4 4 3 1 2 0 114 4 1

Geometric Standard Deviation 2 1 3 4 2 3 4 5 3 4 3 2 2 4 5

Min 38 93 38 1 10 1 0 0 1 0 1 0 38 0 0

5% 38 93 38 1 10 1 0 0 1 0 1 0 38 0 0

10% 38 93 38 1 10 1 1 0 1 0 1 0 38 1 0

25% 93 93 38 1 10 1 2 2 2 0 1 0 93 1 0

50% 105 113 97 8 14 1 4 7 3 1 1 0 105 6 1

75% 120 120 457 14 35 6 10 14 4 1 4 1 120 14 3

90% 457 120 457 35 35 6 15 15 31 4 13 1 457 15 6

95% 457 120 457 35 35 6 31 15 31 13 13 1 457 35 31

Max 457 120 457 35 35 6 31 15 31 13 13 1 457 35 31



### Table 5. Summary statistics for norma lized inhalation concentration ((mg/m 3 

### )/lb AI) using empirical sampling model.

Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent ional Reduced Splash

Arithmetic Mean 0.0347 0.0388 0.0305 0.0076 0.0121 0.0030 0.0106 0.0175 0.0037 0.0124 0.0189 0.0058 0.0347 0.0170 0.0044

Arithmetic Standard Deviation 0.0058 0.0041 0.0038 0.0090 0.0119 0.0005 0.0117 0.0132 0.0034 0.0151 0.0197 0.0033 0.0058 0.0151 0.0031

Geometric Mean 0.0343 0.0387 0.0303 0.0052 0.0089 0.0030 0.0057 0.0121 0.0027 0.0078 0.0120 0.0051 0.0343 0.0113 0.0035

Geometric Standard Deviation 1.1858 1.1138 1.1376 2.3129 2.5264 1.1635 3.4127 3.0232 2.3450 2.6313 3.0588 1.8229 1.1858 2.7484 2.0072

Min 0.0262 0.0343 0.0262 0.0027 0.0051 0.0027 0.0010 0.0017 0.0010 0.0019 0.0019 0.0022 0.0262 0.0017 0.0010

5% 0.0262 0.0343 0.0262 0.0027 0.0051 0.0027 0.0010 0.0017 0.0010 0.0019 0.0019 0.0022 0.0262 0.0017 0.0010

10% 0.0262 0.0343 0.0262 0.0027 0.0051 0.0027 0.0013 0.0017 0.0010 0.0022 0.0019 0.0022 0.0262 0.0019 0.0013

25% 0.0322 0.0343 0.0262 0.0028 0.0051 0.0027 0.0018 0.0076 0.0013 0.0035 0.0081 0.0035 0.0322 0.0053 0.0022

50% 0.0337 0.0399 0.0322 0.0043 0.0053 0.0028 0.0059 0.0146 0.0027 0.0080 0.0130 0.0053 0.0337 0.0131 0.0035

75% 0.0399 0.0423 0.0331 0.0053 0.0259 0.0036 0.0146 0.0331 0.0042 0.0130 0.0202 0.0079 0.0399 0.0259 0.0071

### 9 Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent ional Reduced Splash

90% 0.0423 0.0423 0.0331 0.0259 0.0259 0.0036 0.0331 0.0337 0.0101 0.0202 0.0571 0.0107 0.0423 0.0337 0.0101

95% 0.0423 0.0423 0.0331 0.0259 0.0259 0.0036 0.0337 0.0337 0.0101 0.0571 0.0571 0.0107 0.0423 0.0571 0.0107

Max 0.0423 0.0423 0.0331 0.0259 0.0259 0.0036 0.0337 0.0337 0.0101 0.0571 0.0571 0.0107 0.0423 0.0571 0.0107



### Table 6. Summary statistics for normalized inhalati on dose (mg/lb AI) using empirical sampling model.

Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent ional Reduced Splash

Arithmetic Mean 0.0093 0.0086 0.0099 0.0011 0.0016 0.0006 0.0017 0.0027 0.0008 0.0011 0.0013 0.0009 0.0093 0.0019 0.0008

Arithmetic Standard Deviation 0.0009 0.0006 0.0007 0.0009 0.0012 0.0000 0.0018 0.0022 0.0007 0.0010 0.0013 0.0006 0.0009 0.0017 0.0005

Geometric Mean 0.0092 0.0086 0.0099 0.0009 0.0013 0.0006 0.0011 0.0019 0.0006 0.0008 0.0008 0.0008 0.0092 0.0013 0.0007

Geometric Standard Deviation 1.1045 1.0700 1.0757 1.8321 2.0497 1.0161 2.9094 2.6705 2.3240 2.3476 2.9358 1.9434 1.1045 2.6982 1.9286

Min 0.0080 0.0080 0.0094 0.0006 0.0008 0.0006 0.0003 0.0003 0.0003 0.0002 0.0002 0.0004 0.0080 0.0002 0.0003

5% 0.0080 0.0080 0.0094 0.0006 0.0008 0.0006 0.0003 0.0003 0.0003 0.0002 0.0002 0.0004 0.0080 0.0002 0.0003

10% 0.0080 0.0080 0.0094 0.0006 0.0008 0.0006 0.0003 0.0003 0.0003 0.0004 0.0002 0.0004 0.0080 0.0003 0.0003

25% 0.0086 0.0080 0.0094 0.0007 0.0008 0.0006 0.0003 0.0015 0.0003 0.0005 0.0005 0.0005 0.0086 0.0006 0.0004

50% 0.0093 0.0086 0.0096 0.0007 0.0011 0.0007 0.0014 0.0023 0.0005 0.0008 0.0008 0.0009 0.0093 0.0015 0.0007

75% 0.0096 0.0092 0.0107 0.0011 0.0030 0.0007 0.0024 0.0028 0.0012 0.0015 0.0017 0.0014 0.0096 0.0028 0.0013

90% 0.0107 0.0092 0.0107 0.0030 0.0030 0.0007 0.0028 0.0067 0.0020 0.0017 0.0038 0.0016 0.0107 0.0038 0.0016

95% 0.0107 0.0092 0.0107 0.0030 0.0030 0.0007 0.0067 0.0067 0.0020 0.0038 0.0038 0.0016 0.0107 0.0067 0.0020

Max 0.0107 0.0092 0.0107 0.0030 0.0030 0.0007 0.0067 0.0067 0.0020 0.0038 0.0038 0.0016 0.0107 0.0067 0.0020



### Table 7. Summary statistics for normalized inhalation 8-hour time weighted average concentration ((mg/m 3 

### )/lb AI) using empirical sampling model.

Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent ional Reduced Splash

Arithmetic Mean 0.0012 0.0011 0.0012 0.0001 0.0002 0.0001 0.0002 0.0003 0.0001 0.0001 0.0002 0.0001 0.0012 0.0002 0.0001

Arithmetic Standard Deviation 0.0001 0.0001 0.0001 0.0001 0.0002 0.0000 0.0002 0.0003 0.0001 0.0001 0.0002 0.0001 0.0001 0.0002 0.0001

### 10 Statistic 1a 1aCP 1aRS 1b 1bCP 1bRS 2 2CP 2RS 3 3CP 3RS Bottle Convent ional Reduced Splash

Geometric Mean 0.0012 0.0011 0.0012 0.0001 0.0002 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0001 0.0012 0.0002 0.0001

Geometric Standard Deviation 1.1045 1.0700 1.0757 1.8321 2.0497 1.0161 2.9094 2.6705 2.3240 2.3476 2.9358 1.9434 1.1045 2.6982 1.9286

Min 0.0010 0.0010 0.0012 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0010 0.0000 0.0000

5% 0.0010 0.0010 0.0012 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0010 0.0000 0.0000

10% 0.0010 0.0010 0.0012 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0010 0.0000 0.0000

25% 0.0011 0.0010 0.0012 0.0001 0.0001 0.0001 0.0000 0.0002 0.0000 0.0001 0.0001 0.0001 0.0011 0.0001 0.0000

50% 0.0012 0.0011 0.0012 0.0001 0.0001 0.0001 0.0002 0.0003 0.0001 0.0001 0.0001 0.0001 0.0012 0.0002 0.0001

75% 0.0012 0.0011 0.0013 0.0001 0.0004 0.0001 0.0003 0.0003 0.0001 0.0002 0.0002 0.0002 0.0012 0.0003 0.0002

90% 0.0013 0.0011 0.0013 0.0004 0.0004 0.0001 0.0003 0.0008 0.0003 0.0002 0.0005 0.0002 0.0013 0.0005 0.0002

95% 0.0013 0.0011 0.0013 0.0004 0.0004 0.0001 0.0008 0.0008 0.0003 0.0005 0.0005 0.0002 0.0013 0.0008 0.0003

Max 0.0013 0.0011 0.0013 0.0004 0.0004 0.0001 0.0008 0.0008 0.0003 0.0005 0.0005 0.0002 0.0013 0.0008 0.0003



### The summary statistics shown in Tables 1 to 4 show that the results for the four dermal scenarios (long dermal, short dermal, long short dermal, and hands only) are very similar. Th is is reflected by the fact that the dermal exposures are dominated by the large measured values on the hands. The results for Tables 1 to 7 also show that the statistics for groups 1aCP and 1aRS are quite similar, especially in view of the fact that they are on ly based on 3 workers per group, and that there are big differences between 1bCP and 1bRS. The differences between the conventional pour and reduced splash exposures are relatively small w ithin groups 2 and 3. The results show some large differences between groups 1b, 2 and 3, especially between dermal exposures in groups 1b and 2.

To evaluate the differences between the groups, an analysis of variance was used to test for statistically significant differences. The following statistical mixed model fitted to al l the exposure data (separat ely for each exposure route) was used for this test: Log(normalized exposure) = group + worker + error For this model, the (fixed effect) grou p variable is the group category that a llocates each exposure measurement to one of the eight groups 1aCP, 1aRS, 1bCP, 1bRS, 2CP, 2RS, 3CP, 3RS. Thus the geometric mean depends upon the container size category (1a, 1b, 2 or 3) and the type of cont ainer (conventional or reduced sp lash). The worker term is a random effect that represents the correlation between mu ltiple measurements on the same worker; each worker has their own random exposure effect that is added to the overall group mean (after ta king logarithms). The worker effects are drawn from a normal distribution with mean zero. Each of the 36 measurements also has a random error term drawn from another normal distribution with mean zero. This mode l was fitted to the data and then used to test for the following differences between the eight groups using a statistical contrast:

• RS=CP for bottles. This tests if th e means for groups 1aCP and 1aRS ar e equal. A non-significant difference supports combining the 1a data from conve ntional and reduced splash containers.

### 11 

### • RS=CP for other. This tests if th e means for groups 1bCP and 1bRS are equal, and the means for groups 2CP and 2RS are equal, and the means for groups 3CP and 3RS are equal. A non-signifi cant difference supports combining the data from conventional and reduced splash containers of the same size, when the receiving container is not a trigger spray bottle. It does not evaluate whether the size groups 1b, 2, and 3 can be combined.

• 1b=2=3 for CP. This tests if the means for groups 1bCP, 2CP, and 3CP are equal. A non-significant difference supports combining the conventional pour data from c ontainers of difference sizes, when the receiving container is not a trigger spray bottle.

• 1b=2=3 for RS. This tests if the means for groups 1bRS, 2RS, and 3RS are equal. A non-significant difference supports combining the reduced splash da ta from containers of difference si zes, when the receiving container is not a trigger spray bottle.

• bottles=other for CP. This tests if the means for groups 1aCP, 1bCP, 2CP, and 3CP are equal. A non-significant difference supports combining the conve ntional pour data from containers of difference sizes, and whether or not the receiving container is a trigger spray bottle.

• bottles=other for RS. This tests if the means for groups 1aRS, 1bRS, 2RS, and 3RS are equal. A non-significant difference supports combining the reduced splash data from containers of difference sizes, and whether or not the receiving container is a trigger spray bottle.

The results are shown in Table 8. P-values at or below 0.05 indicate statistically si gnificant differences at the 5 percent significance level. The “RS=CP for bottles ” test is not significant for all the e xposure routes, which supports combining the group 1a data for CP and RS into a single group. The “1b= 2=3 for CP” test is significant for the dermal exposures but not for the inhalation exposures, whic h fails to support combining the CP data for the different container sizes. The “1b=2=3 for RS” test is significant for the dermal exposures but not for the inhalation e xposures, which fails to support combining the RS data for the different container sizes. Th e “bottles=other for CP” test is significant for all the exposure routes except for the inhalati on concentration, which fails to support co mbining the CP data for the different container sizes and for pouring into tri gger spray bottles. The “bottles=other fo r RS” test is significant for all the exposure routes, which fails to support combining the RS da ta for the different containe r sizes and for pouring into trigger spray bottles. Despite these findi ngs, it is not feasible to apply separa te unit exposure estimates (and, ultimately, regulatory decisions) for pouring li quids from containers of di fferent sizes, so it was decide d that the three groups 1b, 2, and 3 would be combined for the statistical mixed modeli ng. Under the mixed models, the geometric mean exposure is assumed to be the same for groups 1b, 2 and 3 (although di fferent between conventional pour and reduced splash containers) and any differences between c ontainer size groups are treated as be ing part of the random variability in exposure. Therefore the final mixed mode ls used three groups only:- Bottle: 1a -Pouring into trigger spray bottles; Conventional: 1bCP, 2CP, and 3CP-Pouri ng from conventional pour containers not into trigger spray bottles; and Reduced Splash: 1bRS, 2RS, and 3RS-Pouring from reduced splash containers not in to trigger spray bottles. Table 8. Statistical tests comp aring different groups of s ource and receiving containers.
Normalized Exposure Test P-Value
Long Dermal mg per pound AI RS=CP for bottles 0.88
Long Dermal mg per pound AI RS=CP for other 0.01
Long Dermal mg per pound AI bottles=other for CP 0.00
Long Dermal mg per pound AI bottles=other for RS 0.00

### 12 Normalized Exposure Test P-Value
Long Dermal mg per pound AI 1b=2=3 for CP 0.02
Long Dermal mg per pound AI 1b=2=3 for RS 0.00
Short Dermal mg per pound AI RS=CP for bottles 0.84
Short Dermal mg per pound AI RS=CP for other 0.03
Short Dermal mg per pound AI bottles=other for CP 0.00
Short Dermal mg per pound AI bottles=other for RS 0.00
Short Dermal mg per pound AI 1b=2=3 for CP 0.01
Short Dermal mg per pound AI 1b=2=3 for RS 0.03
Long Short Dermal mg per pound AI RS=CP for bottles 0.87
Long Short Dermal mg per pound AI RS=CP for other 0.01
Long Short Dermal mg per pound AI bottles=other for CP 0.00
Long Short Dermal mg per pound AI bottles=other for RS 0.00
Long Short Dermal mg per pound AI 1b=2=3 for CP 0.01
Long Short Dermal mg per pound AI 1b=2=3 for RS 0.00
Hands Only Dermal mg per pound AI RS=CP for bottles 0.86
Hands Only Dermal mg per pound AI RS=CP for other 0.01
Hands Only Dermal mg per pound AI bottles=other for CP 0.00
Hands Only Dermal mg per pound AI bottles=other for RS 0.00
Hands Only Dermal mg per pound AI 1b=2=3 for CP 0.03
Hands Only Dermal mg per pound AI 1b=2=3 for RS 0.00
Inhalation Concentration mg/m3 per pound AI RS=CP for bottles 0.74
Inhalation Concentration mg/m3 per pound AI RS=CP for other 0.03
Inhalation Concentration mg/m3 per pound AI bottles=other for CP 0.22
Inhalation Concentration mg/m3 per pound AI bottles=other for RS 0.02
Inhalation Concentration mg/m3 per pound AI 1b=2=3 for CP 0.89
Inhalation Concentration mg/m3 per pound AI 1b=2=3 for RS 0.45
Inhalation Dose mg per pound AI RS=CP for bottles 0.83
Inhalation Dose mg per pound AI RS=CP for other 0.10
Inhalation Dose mg per pound AI bottles=other for CP 0.01

### 13 Normalized Exposure Test P-Value
Inhalation Dose mg per pound AI bottles=other for RS 0.00
Inhalation Dose mg per pound AI 1b=2=3 for CP 0.22
Inhalation Dose mg per pound AI 1b=2=3 for RS 0.80
Inhalation 8hr TWA mg/m3 per pound AI RS=CP for bottles 0.83
Inhalation 8hr TWA mg/m3 per pound AI RS=CP for other 0.10
Inhalation 8hr TWA mg/m3 per pound AI bottles=other for CP 0.01
Inhalation 8hr TWA mg/m3 per pound AI bottles=other for RS 0.00
Inhalation 8hr TWA mg/m3 per pound AI 1b=2=3 for CP 0.22
Inhalation 8hr TWA mg/m3 per pound AI 1b=2=3 for RS 0.80



### The statistical analyses use the followi ng three alternative statistical models. Let X be the normalized exposure and X = exp(Y) so that Y = log (X), where log denotes the natural logarithm. LnGM is the log of the geometric mean for a given group. Let Z95 be the 95 th 

### percentile of a standard norma l distribution, approximately 1.645.

• Empirical simple random sampling model. Code “s.” A ssumes that all the values of X from a given group g were randomly drawn from an unspeci fied distribution. Ignores within-w orker correlations. Gives empirical estimates such as in Tables 1 to 7 above.

o Each of the following statistics depends upon the group g and only uses the X and Y values from that group

o Y = LnGM + Error. Error is independent and identic ally distributed with mean 0 and a variance that depelognormal nds upon the group g.

o AMs = Arithmetic mean of X values

o GMs = Geometric mean of X values = exp(LnGM) (= GMu)

o GSDs = Geometric standard deviation of X values (= GSDu)

o P95s = 95 th 

### percentile of X values

• Lognormal simple random sampling model. Code “u.” Assu mes that all the values of X from a given group g were randomly drawn from a log-normal distri bution. Ignores within -worker correlations.

o Each of the following statistics depends upon the group g and only uses the X and Y values from that group

o Y = LnGM + Error. Error is normall y distributed with mean 0, variance Vu, and stan dard deviation Su = √ Vu.

o AMu = Modeled arithmetic mean of X values = exp(LnGM) exp(1⁄2 Vu)

o GMu = Modeled geometric mean of X values = exp(LnGM)

o GSDu = Modeled geometric standard deviation of X values = exp(Su)

### 14 

### o P95u = Modeled 95 th 

### percentile of X values = exp(LnGM) exp(Z95×Su)

• Lognormal mixed model. Code “m.” There are three gr oups, Bottle, Conventional Pour, and Reduced Splash, as defined above. Each group has a different geometric mean. Assumes that the 18 worker random effects were independently randomly drawn from a normal distri bution and that the 36 random error terms were independently drawn from another normal distribu tion. The error term for each worker and exposure measurement is the sum of the worker effect for th at worker and the within-w orker random error term.

o Y = LnGM + Worker + Error. Worker is normally distributed with mean 0, variance Vw, and standard deviation Sw = √ Vw. Error is normally distributed with mean 0, variance Vr, and st andard deviation Sr

= √ Vr. Define V = Vw + Vr and S = √ V. V is the variance of Y, and S is the standard deviation of Y. LnGM depends upon the group.

o ICC = Intra-worker correlation coefficient = Vw/V.

o AMm = Modeled arithmetic mean of X values = exp(LnGM) exp(1⁄2 V). Depends upon the group.

o GMm = Modeled geometric mean of X values = exp(LnGM). Depends upon the group.

o GSDm = Modeled geometric standard deviation of X values = exp(S)

o P95m = Modeled 95 th 

### percentile of X values = exp(LnGM ) exp(Z95×S). Depends upon the group. For the lognormal mixed model, the ICC value estimates th e clustering effect of multiple measurements on the same worker and lies between 0 (no clustering) and 1 (complete clustering and negligible within-cluster variation). An ICC of 0 is when repeated measurements on the same worker are uncorrelated. An ICC of 1 is when all the exposure measurements on the same worker are identical. Table 9 presents the arithmetic mean and 95 th 

### percentile estimates from the lognorma l mixed model, together with 95% confidence intervals, for all the exposur e routes. These are the values of AMm and P95m. The other summary statistics are presented in more detail below.

Table 9. Arithmetic mean and 95 th 

### percentile estimates from lognormal mixed model for normalized exposure.

Exposure Route Clothing Group Arithmetic Mean (95% confidence interval) 95 th 

### percentile (95% confidence interval) Dermal (mg/lb AI) Long pants and long sleeves Bottle 298.5 (89.9, 1005.7) 1105.5 (309.4, 3817.5) Conventional 10.0 (4,5. 22.8) 36.9 (15.4, 86.7) Reduced Splash 3.1 (1.4, 7.4) 11.6 (4.9, 28.1) Short pants and short sleeves Bottle 207.4 (77.3, 568.3) 706.5 (241.3, 2009.2)

Conventional 9.0 (4,7. 17.6) 30.7 (14.6, 63.2) Reduced Splash 4.0 (2.1, 7.9) 13.6 (6.4, 28.7) Long pants and short sleeves Bottle 280.7 (89.5, 892.7) 1020.9 (300.8, 3350.0) Conventional 9.9 (4.7, 21.7) 36.0 (15.6, 81.8)

### 15 

### Exposure Route Clothing Group Arithmetic Mean (95% confidence interval) 95 th 

### percentile (95% confidence interval) Reduced Splash 3.0 (1.4, 6.8) 11.0 (4.8, 25.7) Hands only Bottle 314.0 (89.8, 1115.2) 1178.7 (315.1, 4245.5) Conventional 10.3 (4.5, 24.6) 38.8 (15.7, 93.7) Reduced Splash 3.1 (1.3, 7.5) 11.4 (4.6, 28.6) Inhalation Concentration (mg/m 3 

### /lb AI) Bottle 0.047 (0.024, 0.093) 0.128 (0.061, 0.264)

Conventional 0.016 (0.010, 0.024) 0.042 (0.025, 0.071) Reduced Splash 0.0049 (0.0032, 0.0076) 0.0132 (0.0079, 0.0223) Inhalation Dose (mg/lb AI) Bottle 0.012 (0.006, 0.024) 0.033 (0.016, 0.066)

Conventional 0.0017 (0.0011, 0.0026) 0.0046 (0.0028, 0.0075) Reduced Splash 0.00091 (0.00061, 0.00140) 0.00242 (0.00148, 0.00401) Inhalation 8-hr TWA (mg/m 3 

### /lb AI) Bottle 0.0016 (0.0008, 0.0030) 0.0041 (0.0020, 0.0083)

Conventional 0.00021 (0.00014, 0.00033) 0.00057 (0.00035, 0.00093) Reduced Splash 0.00011 (0.00008, 0.00018) 0.00030 (0.00019, 0.00050)

For each exposure route, the above three statistical models we re fitted to the observed data and the summary statistics listed above were calculated together w ith 95% confidence intervals. The 95% confidence intervals in Table 9 were computed using a parametric bootstrap. For these calculations, the parametric bootstrap simulations were all generated from the fitted lognormal mixed model, even for the empi rical and simple random sample summary statistics, on the basis that the mixed model is the best choice for modeling the data, even if the summary stat istics are developed from a simpler statistical model. For example, in Tables 1 to 7, the empirical arithmetic mean s are presented, which are the arithmetic means of the group measurements (between 3 a nd 15 measurements per group). To estimate the uncertainty of those empirical arithmetic means, data are simulated from the lognormal mi xed model to calculate the parametric bootstrap confidence intervals. The arithm etic means in Table 9 are estimated using the lognormal mixed model, which is also used to estimate the confidence intervals in Ta ble 9. The unit exposure estimates (from the lognormal mixed model) displayed in Table 9 are recommended over the empirical arithmetic means and 95 th 

### percentiles displayed in Tables 1 to 7. (For the original groupings the deta iled results in Tables 1 to 7 may be preferable). The algorithm used was as follows:
Step 1:

### 16 Simulate 36 random variables Y, X from the estimated lognormal distribution superimposed upon the observed sampling structure - --; W = RanNor (Seed) ×Sw (18 values, one for each worker) Y = W + LnGM + RanNor(Seed)×Sr X = exp(Y)
where: LnGM = group intercept of mixed effect log-log regression model Sw = square root of between worker variance Sr = square root of within worker variance under mixed-effect model
The allocation of each worker to two group s (one for each measurement) is exactly the same as the observed random design configuration.
Step 2:

For Y:

Calculate GMs = exp(EAM)
Calculate GSDs = exp(Su)
Calculate AMu = GMs×exp(0.5×Su×Su)
Calculate P95u = GMs× exp(Z95×Su) Fit mixed lognormal model to simulated Y values

Under mixed-effects model:

Calculate GMm = exp(group intercept of mixed-effects model)
Calculate GSDm = exp(square root (total variance V under mixed-effects model))
Calculate ICC = Vw /V Calculate AMm = exp(group intercept + 0.5×V) Calculate P95m = exp(group intercept + Z95×S)

where:
EAM = sample arithmetic mean of Y over group = AMu Su = standard deviation of Y over group
V = total variance under mixed-effects model S = square root of V
Vw = between worker variance.

For X:
Calculate arithmetic mean for group AMs
Calculate 95 th percentile for group P95s Step 3: Repeat Steps 1 and 2 10,000 times.
Steps 1 to 3 result in 10,000 values each for each of GSDs, GMs, GMm, AMs, AMm, AMu, P95s, P95m , and P95u for each group and 10 ,000 values each for GSDm and ICC. 95% confidence inte rvals can be defined for each parameter by the 2.5 th and 97.5 th percentiles (lower and upper, respectively) of the bootstrap distribution of that corres ponding parameter. Note that by definition, GSDs = GSDu and GM s = GMu.

### 17 

### The dermal exposure results in Table 9 based on the l ognormal mixed model show that for all three groups the arithmetic mean for long pants and long sl eeves is higher than the ar ithmetic mean for long pants and short sleeves, and that for the Bottle and Conventional groups the arithmetic m ean for long pants and short sleeves is higher than the arithmetic mean for short pants and short sleeves. These resu lts would appear to be cont rary to the fact that the calculated exposures for short sleeves ve rsus long sleeves are higher due to th e outer dosimeter for the lower arm and the calculated exposures for short pants versus long pants are higher due to the outer dosimeter for the lower leg. These results occurred because the estimated arithmetic mean based on the lognormal mixed model is given by the formula GMm×exp(1⁄2 V) where GMm is the estimated geometric mean and V is the estimated variance. Even if the estimated geometric mean increases, the estimated variance can decr ease producing a net decrease in the estimated arithmetic mean even though the true arithmetic mean must increase. Si nce all three dermal exposure measures for this liquid pour scenario are dominated by the hands onl y exposure, the differences in the estimated arithmetic means and between the estimated 95 th 

### percentiles for the three dermal exposure measures are small compared to the very wide confidence intervals. For this reason we regard this issue as a statistical “quirk” attributable to large uncertainty in the fitted models for dermal exposure. In the section “A lternative models for dermal exposure” we investigate alternative models and outlier treatments to further unde rstand these statistical “quirks.”

Outliers and non-detects For all the analyses presented in th is memorandum, except for Tables 10, 11 a nd 20 (see below for discussion on Table 20), all the data values were used and values below the L OQ were replaced by one half of the LOQ. For three subjects and MEs (Reduced Splash ME 1 in group 1a, Reduced Spla sh ME 7 in group 2, and Conventional Pour ME 6 in group 1b), the hand exposure measurements were much higher wh en normalized by the amount of active ingredient than values for all other subjects in the same group. The liquid po ur scenario is one in whic h unusually large hand exposures can occur through random dripping and spill ing events that may be poorly associ ated with the tota l amount of active ingredient used. To investigate the impact of this poten tial outlier, we recomputed the arithmetic mean and 95 th 

### percentile estimates (and parametric bootstrap confidence intervals) for Long Dermal exposure after excluding the dermal data for these measurements. As shown in Table 10, the mean is reduced by between 29% and 42% (for Bottle using zero substitution) and the 95 th 

### percentile is reduced by between 33% a nd 45% (for Bottle using zero substitution) for Long Dermal exposure. The ou tliers have a substantial effect. Also investigated in Table 10 (for Long Dermal) and in Tabl e 11 (for inhalation concentra tion) is the impact of the values below the LOQ. All th e hand wash in the study were above the L OQ. For the Conventional Pour, 4 of the 18 face and neck measurements, 67 of the 108 outer dosim eter measurements, 107 of the 108 inner dosimeter measurements, and 6 of the 18 OVS measurements were belo w the LOQ. For the Reduced Splash, 0 of the 18 face and neck measurements, 41 of the 108 outer dosimeter measurem ents, 105 of the 108 inner dosimeter measurements, and 9 of the 18 OVS measurements were below the LOQ. For th e Long Dermal exposure we computed the arithmetic mean and 95 th 

### percentiles using the recommended substitution of one half the LOQ for values below the LOQ and compared the estimates using alternative substitu tions of the LOQ (the maximum possible exposure estimate) and of zero (the minimum possible exposure estimate. For the inhalation concentrati on and dose we computed the arithmetic mean and 95 th 

### percentiles using the recommended s ubstitution of one half the LOQ for values below the LOQ and compared the estimates using the alternative substitu tions of the LOQ (the maximum possible exposure estimate); substitution of zero for inhalation exposure is not useful becau se the statistical models use the loga rithms of the exposure which cannot be calculated when the minimum exposure is zero. We also investigated a statisti cal imputation scheme described in the following paragraphs. Note that in some cases replacing non-detect values by zero increased the estimated arithmetic mean and 95 th 

### percentile compared to using the default half LOQ method, and repl acing non-detect values by the LOQ decreased the estimated arithmetic mean and 95 th 

### percentile compared to using th e default half LOQ method. This paradoxical finding occurred because using zero instead of half the LOQ increased the estimated variance and using the LOQ instead of half the

### 18 

### LOQ decreased the estimated variance; the arithmetic mean and 95 th 

### percentile estimates from the mixed model adjust the geometric mean using the estim ated variance of the logarithms. As a more exact approach for analyzing values below the LOQ, a multiple imputation approach using maximum likelihood methods for censored data was applied, as follo ws. Each dermal exposure value is known to be between L and U, where L is the value obtained by replacing all valu es below the LOQ by zero and summing the values for hand wash, face and neck, and the dosimeters, and U is the valu e obtained by replacing all values below the LOQ by the LOQ and summing the values for hand wash, face and neck, a nd the dosimeters. The dermal exposure totals data are thus censored and lie between L and U. Fo r inhalation exposure, the values of L and U are equal to the measured value if it is above the LOQ and are given by L equals zero and U equals the L OQ if the value is below the LOQ. To estimate the unknown values for the dermal exposure, the following mixed model was fitted to the combined censored and uncensored data: Log (Exposure) = Group + Slope × Log (Pounds of Active Ingredient) + Worker + Error In this model, the value of Slope is not necessarily 1, Gr oup is a fixed effect value for each of the three groups Bottle, Conventional, and Reduced Splash giving the intercept for each group, Worker is a normally distributed random effect variable with independent, identically distributed values for each worker, a nd Error is a normally distributed error variable with independent, identically di stributed values for each total exposure measurement. Note that this model ignores any information in the data about which of the values were non-detects. This model was fitted using the SAS procedure NLMIXED, using code adapted from the article “Analysis of Lognormally Dist ributed Exposure Data with Repeated Measures and Values below the Limit of Detection Using SAS” (YAN JIN, MISTY J. HEIN, JAMES A. DEDDENS and CYNTHIA J. HINES, Ann Occup Hyg (2011) 55(1): 97-112, doi:10.1093/annhyg/meq061). For these calculations, the marginal likelihood averaged over the rando m effects is maximized. The fitted model has values for the following parameters: three Group intercepts, Slope, Varian ce of Worker, Variance of Error. Separate models were fitted for each clothing and inhalation scenario.
Exposure values were randomly generate d from the fitted model by first si mulating the eighteen Worker random effects, and then simulating values for the random error us ing the conditional distribution given that the total exposure for each censored value is between L and U. Uncensored va lues (where all components were above the LOQ) were not changed. In this manner, all 36 exposure values for a given scenario were simulated. To ac count for the uncertainty in the simulations, the entire simulation was repeated 5 times for each scenario, producing 5 independent imputation data sets. For the multiple imputation data, each statistic and confidence bound was averaged over the fi ve imputations to give an overall average statistic and confidence in terval. Note that this a pproach does not fully account for the uncertainty due to the imputation. Instead, the Bayesian me thods of Rubin might have been used to account for the variance from the imputation, but those methods use the standard errors of the st atistics rather than the confidence intervals, and so would ignore the skewness in the estimated para metric bootstrap confidence intervals. Table 10. Long Dermal summary statistics calculated with and without the potential outlier data for Reduced Splash ME 1 in group 1a, Reduced Splash ME 7 in group 2, and Conventional Pour ME 6 in group 1b, and using alternative estimated exposures for values below the LOQ.

### 19 

### Group Data Method for substituting values below the LOQ Arithmetic mean (mg / lb AI) 95th percentile (mg / lb AI)

Bottle All 36 Values Substitute 1⁄2 LOQ 298.5 (89.9, 1005.7) 1105.5 (309.4, 3817.5)

Bottle All 36 Values Substitute LOQ 288.3 (90.1, 932.9) 1055.0 (305.7, 3515.3)

Bottle All 36 Values Substitute

zero 313.9 (89.8, 1114.2) 1177.9 (314.9, 4241.3)

Bottle All 36 Values Multiple imputation 298.6 (89.7, 1008.3) 1106.2 (309.3, 3818.5)

Bottle Exclude outlier data Substitute 1⁄2 LOQ 177.5 (59.9, 550.7) 616.4 (193.9, 1961.3)

Bottle Exclude outlier data Substitute LOQ 171.1 (60.8, 520.0) 592.9 (193.7, 1820.6)

Bottle Exclude outlier data Substitute

zero 183.5 (59.8, 597.7) 651.2 (196.5, 2173.3)

Bottle Exclude outlier data Multiple imputation 177.6 (59.4, 553.8) 618.2 (194.0, 1981.6)

Conventional All 36 Values Substitute 1⁄2 LOQ 10.0 (4.5, 22.8) 36.9 (15.4, 86.7)

Conventional All 36 Values Substitute LOQ 9.7 (4.5, 21.5) 35.5 (15.2, 81.5)

Conventional All 36 Values Substitute

zero 10.4 (4.5, 24.6) 38.8 (15.7, 93.8)

Conventional All 36 Values Multiple imputation 10.0 (4.5, 22.9) 37.0 (15.4, 86.9)

Conventional Exclude outlier data Substitute 1⁄2 LOQ 7.1 (3.5, 14.8) 24.6 (11.1, 54.1)

Conventional Exclude outlier data Substitute LOQ 6.9 (3.5, 14.2) 23.6 (10.9, 50.9)

### 20 

### Group Data Method for substituting values below the LOQ Arithmetic mean (mg / lb AI) 95th percentile (mg / lb AI)

Conventional Exclude outlier data Substitute

zero 7.3 (3.5, 16.0) 25.9 (11.4, 59.6)

Conventional Exclude outlier data Multiple imputation 71. (3.5, 14.8) 24.8 (11.2, 55.1)

Reduced Splash All 36 Values Substitute 1⁄2 LOQ 3.1 (1.4, 7.4) 11.6 (4.9, 28.1)

Reduced Splash All 36 Values Substitute LOQ 3.2 (1.5, 7.3) 11.8 (5.0, 27.7)

Reduced Splash All 36 Values Substitute

zero 3.1 (1.3, 7.5) 11.5 (4.7, 28.8)

Reduced Splash All 36 Values Multiple imputation 3.1 (1.4, 7.3) 11.6 (4.8, 28.0)

Reduced Splash Exclude outlier data Substitute 1⁄2 LOQ 2.0 (1.0, 4.1) 6.9 (3.1, 15.0)

Reduced Splash Exclude outlier data Substitute LOQ 2.1 (1.1, 4.1) 7.0 (3.2, 14.8)

Reduced Splash Exclude outlier data Substitute

zero 1.9 (0.9, 4.1) 6.8 (3.0, 15.3)

Reduced Splash Exclude outlier data Multiple imputation 2.0 (1.0, 4.1) 6.9 (3.1, 15.1)

Table 11. Inhalation concentrati on summary statistics calculat ed using alternative estimated exposures for values below the LOQ. Group Data Method for substituting values below the LOQ Arithmetic mean (mg /

m 3 

### /lb AI) 95th percentile (mg /

m 3 

### / lb AI)

Bottle All 36 Substitute 1⁄2 0.047 (0.024, 0.093) 0.128 (0.061, 0.264)

### 21 

### Group Data Method for substituting values below the LOQ Arithmetic mean (mg /

m 3 

### /lb AI) 95th percentile (mg /

m 3 

### / lb AI)

Values LOQ

Bottle All 36 Values Substitute LOQ 0.086 (0.049, 0.150) 0.206 (0.111, 0.377)

Bottle All 36 Values Multiple imputation 0.001 (0.001, 0.002) 0.003 (0.001, 0.007)

Conventional All 36 Values Substitute 1⁄2 LOQ 0.016 (0.010, 0.024) 0.042 (0.025, 0.071)

Conventional All 36 Values Substitute LOQ 0.016 (0.011. 0.023) 0.039 (0.025, 0.060)

Conventional All 36 Values Multiple imputation 0.017 (0.011, 0.029) 0.051 (0.028, 0.090)

Reduced Splash All 36 Values Substitute 1⁄2 LOQ 0.0049 (0.0032, 0.0076) 0.0132 (0.0079, 0.0223) Reduced Splash All 36 Values Substitute LOQ 0.0058 (0.0041, 0.0084) 0.0141 (0.0092, 0.0217)
Reduced Splash All 36 Values Multiple imputation 0.0049 (0.0030, 0.0081) 0.0143 (0.0081, 0.0257)

The results in Tables 10 demonstrate that all the alternativ e approaches for treating values below the LOQ have a very small effect on Long Dermal exposure (the change in the estimates is less than 7%). The results were similar for Short Dermal and Long Short Dermal exposure. The results in Table 11 demonstrate very large impacts of th e alternative approaches for treating values below the LOQ on the inhalation concentration, because of the large percentage of OVS values below the LOQ: For the Bottle group, using the LOQ substitution instead of the half LOQ substitution increases the arithmetic mean and 95 th 

### percentile by up to 81%, and using the multiple imputation instead of the half LOQ substitution decreases the arithmetic mean and 95 th 

### percentile by up to 98%. For the Conventional and Reduced Splash groups, using the LOQ substitution instead of the half LOQ substitution changes the arithmetic mean and 95 th 

### percentile by up to 8%, and using the multiple imputation instead of the half LOQ substitution increases the arithmetic mean and 95 th 

### percentile by up to 20%. The inhalation exposure results were similar for the inhalation dose and the inhalation 8-hour time weight ed average concentration; results not shown.

### 22 

### Fold relative accuracy Fold relative accuracy ( fRA ) is a measure that can be used to determine how well a statistic can describe its population parameter. Let us assume θ is a parameter and T is the sample statistic of θ (i.e., an estimate of θ ). If the 2.5 th 

### and 97.5 th 

### percentiles of the sampling dist ribution of T can be denoted by T 2.5 

### and T 97.5 

### , respectively, then the 95 th 

### percentile of sample fold relative accuracy can be theoretically calculated using the following formula provided in the AHETF Governing Document (AHETF, 2007, pg. 136 and AHETF, 2011, pg. 120): fRA 95 

### = Max (T 97.5 

### / θ , θ / T 2.5 

### )

The actual value of θ is unknown. Thus, fRA 95 

### was calculated by substituting θ with T. If the fRA 95 

### of a statistic were equal to 3, then it would be correct to sa y: “At least 95% of the time the sample statistic will be accurate to within 3- fold of the population value”. Accord ing to the AHETF Governi ng Document, the statistical design of the exposure monitoring study should be adequate to produce a fRA 95 

### less than or equal to 3. Thus the confidence intervals calculated in the above algorithm can be used to estimate the fold relative accuracy and compare th e observed fRA with the study design benchmark of 3. If the observed fold relative accuracy is grea ter than 3, this means that the experiment did not meet the benchmark, which would be due to differences betw een the distributions of the CMA data used to design the study and the experimental data collected in the study. If the fold re lative accuracy benchmark is not met, then it might be desirable to collect more data for this scenario in order to meet the benchmark. Fo ld relative accuracy was not computed for the ICC since the estimated ICC is 0 in many cases. In previously reported statistical analyses, following HSRB recommendations, confidence intervals were estimated using both a parametric bootstra p approach and a non-parametric bootstrap a pproach. For this scenario, non-parametric confidence intervals were not developed because of the difficu lty in accounting for both the worker and group effects in a fully non-parametric framework. Detailed summary statistics with parametric co nfidence intervals and fold relative accuracy Tables 12 to 18 present the estimates, parametric confiden ce intervals and fold relative accuracy values for all the summary statistics for the four dermal and tw elve inhalation exposure routes, respectively. Table 12. Arithmetic mean, geometric mean, geometric standard deviation, and 95 th 

### percentiles (with 95% confidence intervals and fold relative accuracy), fo r different statistical mode ls of the normalized long dermal exposure (mg/lb AI).

Bottle Conventional Reduced Splash

Parameter Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy

GSDs 2.2 1.7 8.7 4.0 4.0 2.3 6.4 1.7 4.3 2.4 6.4 1.8

GSDm 3.9 2.8 5.4 1.4 3.9 2.8 5.4 1.4 3.9 2.8 5.4 1.4

ICC 0.3 0.0 0.7 0.3 0.0 0.7 0.3 0.0 0.7

GMs 116.2 39.5 376.4 3.2 4.1 2.0 8.0 2.0 1.2 0.6 2.5 2.0

GMm 120.0 39.1 370.3 3.1 4.0 2.0 7.9 2.0 1.3 0.6 2.5 2.0

AMs 155.3 63.4 1007.6 6.5 8.4 3.8 24.3 2.9 3.7 1.2 7.6 3.2

AMu 158.1 70.1 1755.5 11.1 10.9 4.1 28.1 2.6 3.6 1.3 8.9 2.8

### 23 Bottle Conventional Reduced Splash

Parameter Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy
AMm 298.5 89.9 1005.7 3.4 10.0 4.5 22.8 2.3 3.1 1.4 7.4 2.3

P95s 459.5 132.4 4287.3 9.3 35.2 11.5 210.6 6.0 31.4 3.6 65.5 8.7

P95u 422.3 183.6 6158.5 14.6 40.9 12.8 106.7 3.2 13.7 4.0 33.8 3.5

P95m 1105.5 309.4 3817.5 3.6 36.9 15.4 86.7 2.4 11.6 4.9 28.1 2.4



### Table 13. Arithmetic mean, geometric mean, geometric standard deviation, and 95 th 

### percentiles (with 95% confidence intervals and fold relative accuracy), fo r different statistical models of the normalized short dermal exposure (mg/lb AI).

Bottle Conventional Reduced Splash

Parameter Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy

GSDs 2.2 1.6 6.2 2.8 3.7 2.1 4.8 1.8 3.0 2.1 4.7 1.6

GSDm 3.1 2.3 4.2 1.3 3.1 2.3 4.2 1.3 3.1 2.3 4.2 1.3

ICC 0.4 0.0 0.7 0.4 0.0 0.7 0.4 0.0 0.7

GMs 118.6 41.7 288.4 2.8 4.6 2.7 8.4 1.8 2.0 1.2 3.7 1.8

GMm 108.1 42.2 279.0 2.6 4.7 2.7 8.3 1.8 2.1 1.2 3.7 1.8

AMs 157.8 60.0 583.7 3.7 9.1 4.2 18.4 2.2 4.2 1.9 8.1 2.3

AMu 160.7 64.3 828.4 5.2 10.7 4.5 20.0 2.4 3.7 1.9 8.8 2.4

AMm 207.4 77.3 568.3 2.7 9.0 4.7 17.6 2.0 4.0 2.1 7.9 2.0

P95s 464.6 114.9 2175.6 4.7 40.0 11.5 130.2 3.5 32.2 5.1 59.7 6.3

P95u 427.9 151.8 3060.5 7.2 39.0 12.5 75.6 3.1 12.1 5.5 33.2 2.7

P95m 706.5 241.3 2009.2 2.9 30.7 14.6 63.2 2.1 13.6 6.4 28.7 2.1



### Table 14. Arithmetic mean, geometric mean, geometric standard deviation, and 95 th 

### percentiles (with 95% confidence intervals and fold relative accuracy), for different statistical models of the normalized long short dermal exposure (mg/lb AI).

Bottle Conventional Reduced Splash

Parameter Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy

### 24 Bottle Conventional Reduced Splash

Parameter Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy

GSDs 2.2 1.7 7.9 3.6 3.6 2.3 5.9 1.6 4.2 2.3 5.9 1.8

GSDm 3.6 2.6 5.0 1.4 3.6 2.6 5.0 1.4 3.6 2.6 5.0 1.4

ICC 0.3 0.0 0.7 0.3 0.0 0.7 0.3 0.0 0.7

GMs 116.7 42.0 364.5 3.1 4.4 2.2 8.3 2.0 1.3 0.7 2.5 1.9

GMm 121.6 41.3 357.2 2.9 4.3 2.2 8.3 1.9 1.3 0.7 2.5 1.9

AMs 155.8 65.1 896.8 5.8 8.5 4.0 23.1 2.7 3.8 1.2 7.0 3.1

AMu 158.5 71.4 1477.6 9.3 10.1 4.3 26.1 2.6 3.7 1.3 8.0 2.8

AMm 280.7 89.5 892.7 3.2 9.9 4.7 21.7 2.2 3.0 1.4 6.8 2.2

P95s 461.2 133.5 3704.9 8.0 35.2 11.8 190.7 5.4 31.5 3.6 57.8 8.8

P95u 423.1 181.4 5285.8 12.5 36.6 13.0 99.5 2.8 13.8 3.9 30.6 3.5

P95m 1020.9 300.8 3350.0 3.4 36.0 15.6 81.8 2.3 11.0 4.8 25.7 2.3



### Table 15. Arithmetic mean, geometric mean, geometric standard deviation, and 95 th 

### percentiles (with 95% confidence intervals and fold relative accuracy), fo r different statistical mode ls of the normalized hands only exposure (mg/lb AI).

Bottle Conventional Reduced Splash

Parameter Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy

GSDs 2.2 1.8 9.4 4.2 4.2 2.4 6.8 1.7 4.6 2.4 6.8 1.9

GSDm 4.1 2.9 5.7 1.4 4.1 2.9 5.7 1.4 4.1 2.9 5.7 1.4

ICC 0.2 0.0 0.6 0.2 0.0 0.6 0.2 0.0 0.6

GMs 113.6 37.3 385.3 3.4 4.0 1.9 8.0 2.1 1.1 0.6 2.3 2.0

GMm 118.0 37.0 379.2 3.2 3.9 1.9 7.9 2.0 1.1 0.6 2.3 2.0

AMs 153.1 61.4 1111.4 7.3 8.3 3.8 26.1 3.2 3.6 1.1 7.7 3.4

AMu 156.3 68.8 2027.0 13.0 11.1 4.1 31.0 2.8 3.6 1.2 9.2 3.1

AMm 314.0 89.8 1115.2 3.6 10.3 4.5 24.6 2.4 3.1 1.3 7.5 2.4

P95s 456.9 131.8 4862.3 10.6 35.0 11.6 235.2 6.7 31.3 3.4 68.1 9.2

P95u 422.5 182.1 7036.8 16.7 42.1 12.9 116.7 3.3 14.0 3.8 34.7 3.7

### 25 Bottle Conventional Reduced Splash

Parameter Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy
P95m 1178.7 315.2 4245.5 3.7 38.8 15.7 93.7 2.5 11.4 4.6 28.6 2.5



### Table 16. Arithmetic mean, geometric mean, geometric standard deviation, and 95 th 

### percentiles (with 95% confidence intervals and fold relative accuracy), for different stat istical models of the normalized inhalation concentration (mg/m 3 

### /lb AI).

Bottle Conventional Reduced Splash

Parameter Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy

GSDs 1.1858 1.3981 3.6254 3.1 2.7484 1.6565 2.9691 1.7 2.0072 1.6592 2.9904 1.5

GSDm 2.2311 1.8484 2.7008 1.2 2.2311 1.8484 2.7008 1.2 2.2311 1.8484 2.7008 1.2

ICC 0.0000 0.0000 0.4762 0.0000 0.0000 0.4762 0.0000 0.0000 0.4762

GMs 0.0343 0.0180 0.0651 1.9 0.0113 0.0076 0.0171 1.5 0.0035 0.0024 0.0053 1.5

GMm 0.0343 0.0178 0.0655 1.9 0.0113 0.0076 0.0171 1.5 0.0035 0.0024 0.0053 1.5

AMs 0.0347 0.0220 0.0929 2.7 0.0170 0.0097 0.0245 1.8 0.0044 0.0030 0.0076 1.7

AMu 0.0348 0.0229 0.1045 3.0 0.0189 0.0099 0.0253 1.9 0.0045 0.0031 0.0079 1.8

AMm 0.0473 0.0240 0.0930 2.0 0.0156 0.0102 0.0243 1.6 0.0049 0.0032 0.0076 1.6

P95s 0.0423 0.0377 0.2912 6.9 0.0571 0.0211 0.1184 2.7 0.0107 0.0065 0.0373 3.5

P95u 0.0453 0.0453 0.3503 7.7 0.0598 0.0225 0.0785 2.7 0.0111 0.0070 0.0249 2.2

P95m 0.1283 0.0613 0.2640 2.1 0.0424 0.0253 0.0705 1.7 0.0132 0.0079 0.0223 1.7



### Table 17. Arithmetic mean, geometric mean, geometric standard deviation, and 95 th 

### percentiles (with 95% confidence intervals and fold relative accuracy), fo r different statistical models of the normalized inhalation dose (mg/lb AI).

Bottle Conventional Reduced Splash

Parameter Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy

GSDs 1.1045 1.3829 3.4757 3.1 2.6982 1.6294 2.8651 1.7 1.9286 1.6319 2.8850 1.5

GSDm 2.1732 1.8116 2.6143 1.2 2.1732 1.8116 2.6143 1.2 2.1732 1.8116 2.6143 1.2

ICC 0.0000 0.0000 0.4762 0.0000 0.0000 0.4762 0.0000 0.0000 0.4762

### 26 Bottle Conventional Reduced Splash

Parameter Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy

GMs 0.0092 0.0049 0.0172 1.9 0.0013 0.0009 0.0019 1.5 0.0007 0.0005 0.0010 1.5

GMm 0.0092 0.0049 0.0173 1.9 0.0013 0.0009 0.0019 1.5 0.0007 0.0005 0.0010 1.5

AMs 0.0093 0.0060 0.0238 2.6 0.0019 0.0011 0.0026 1.8 0.0008 0.0006 0.0014 1.7

AMu 0.0093 0.0062 0.0266 2.9 0.0021 0.0011 0.0027 1.9 0.0008 0.0006 0.0014 1.7

AMm 0.0125 0.0065 0.0239 1.9 0.0017 0.0011 0.0026 1.5 0.0009 0.0006 0.0014 1.5

P95s 0.0107 0.0101 0.0730 6.8 0.0067 0.0023 0.0123 2.9 0.0020 0.0012 0.0066 3.3

P95u 0.0109 0.0121 0.0873 8.0 0.0065 0.0025 0.0083 2.6 0.0020 0.0013 0.0045 2.2

P95m 0.0330 0.0162 0.0664 2.0 0.0046 0.0028 0.0075 1.7 0.0024 0.0015 0.0040 1.7



### Table 18. Arithmetic mean, geometric mean, geometric standard deviation, and 95 th 

### percentiles (with 95% confidence intervals and fold relative accuracy), for different statistica l models of the normalized inhalation 8-hour time-weighted average (mg/m 3 

### /lb AI).

Bottle Conventional Reduced Splash

Parameter Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy Estimate Lower Bound Upper Bound Fold RelativeAccuracy

GSDs 1.10454 1.38288 3.47565 3.1 2.69819 1.62939 2.86515 1.7 1.92864 1.63191 2.88502 1.5

GSDm 2.17321 1.81159 2.61432 1.2 2.17321 1.81159 2.61432 1.2 2.17321 1.81159 2.61432 1.2

ICC 0.00000 0.00000 0.47616 0.00000 0.00000 0.47616 0.00000 0.00000 0.47616

GMs 0.00115 0.00062 0.00214 1.9 0.00016 0.00011 0.00024 1.5 0.00008 0.00006 0.00013 1.5

GMm 0.00115 0.00061 0.00216 1.9 0.00016 0.00011 0.00024 1.5 0.00008 0.00006 0.00013 1.5

AMs 0.00116 0.00075 0.00298 2.6 0.00024 0.00014 0.00033 1.8 0.00010 0.00007 0.00018 1.7

AMu 0.00116 0.00078 0.00333 2.9 0.00026 0.00014 0.00034 1.9 0.00010 0.00007 0.00018 1.7

AMm 0.00156 0.00081 0.00299 1.9 0.00021 0.00014 0.00033 1.5 0.00011 0.00008 0.00017 1.5

P95s 0.00134 0.00126 0.00913 6.8 0.00084 0.00029 0.00154 2.9 0.00025 0.00015 0.00083 3.3

P95u 0.00136 0.00151 0.01092 8.0 0.00081 0.00031 0.00103 2.6 0.00025 0.00016 0.00056 2.2

P95m 0.00413 0.00202 0.00830 2.0 0.00057 0.00035 0.00093 1.7 0.00030 0.00018 0.00050 1.7

### 27 

### Tables 12 to 18 show that the ICC estimated value is betw een 0.2 and 0.4 for the dermal e xposure routes showing that there is some variation between workers and some corre lation between measurements on the same worker. The ICC values were zero for all the inhalation exposure measures showing no variation between workers. For the Bottle group, most of the dermal exposure measures did not meet the study benchmark design value of 3 for the fold relative accuracy. For the empirical and lognormal simple random sampli ng model, this is partially explained by the fact that the bootstrap confidence intervals were based on a very different statistical model that assumed equal covariance parameters for all three groups, but seve ral of the mixed model parameters al so did not meet the study benchmark design value of 3. A plausible explanati on is that the Bottle data was only based on 6 exposure measurements (although the mixed model was fitted to all 36 measurements). For the inhalation e xposures in the Bottle group, the study benchmark design of 3 for the fold relative accuracy was me t for the summary statistics that used the mixed model. For dermal exposures in the Conventional and Reduced Splash groups, the study benchmark design of 3 for the fold relative accuracy was met for the summary statistics that used the mixed model but was not met for several of the AMs, P95s, and P95u statistics. For inhalation exposures in the Conventional and Reduced Splash groups, the study benchmark design of 3 for the fold relative accur acy was met for all cases except for the empirical 95 th 

### percentile for the Reduced Splash group. Quantile plots Quantile-quantile plots of the normalized exposure values we re used to evaluate whether the data were lognormally distributed, as implied by the assumed st atistical mixed models. In each case th e quantile-quantile plot compared the observed quantiles of the 36 measured values with the correspondi ng quantiles of a normal or lognormal distribution. Since the mixed model assumes that the mean expos ure can depend upon the group, th e corresponding group mean normalized exposure was subtracted from the normalized expos ure when creating the normal distribution plots, and the corresponding group mean logarithm of th e normalized exposure was subtracted fr om the logarithm of the normalized exposure when creating the lognormal dist ribution plots. In this manner the quantile-quantile plots combined all 36 measurements. A perfect fit would imply that the plotted values lie in a strai ght line. The quantil e-quantile plots are presented in Figures 1 to 14. They clearl y show that the lognormal distribution is a better fit than a normal distribution, and that the lognormal distribut ion fits reasonably well for all of the exposure routes.

### 28 

### Figure 1 

### Quantile plot normalized long dermal exposure data with a normal distribution Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3 -200 -100 0 100 200 300 400Normalized Long Dermal Exposure



### Normal Quantiles

### 29 

### Figure 2 

### Quantile plot normalized long dermal exposure data with a lognormal distribution Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 4log (Normalized Long Dermal Exposure)



### Normal Quantiles



### Figure 3


### Quantile plot normalized short dermal exposure data with a normal distribution Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3 -200 -100 0 100 200 300 400Normalized Short Dermal Exposure



### Normal Quantiles

### 30 

### Figure 4 

### Quantile plot normalized short dermal exposure data with a lognormal distribution Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3log (Normalized Short Dermal Exposure)



### Normal Quantiles



### Figure 5
Quantile plot normalized long short dermal exposure data with a normal distribution Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3 -200 -100 0 100 200 300 400Normalized Long Short Dermal Exposure



### Normal Quantiles

### 31 

### Figure 6 

### Quantile plot normalized long short dermal exposure data with a lognormal distribution Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 4lnnrmdermls



### Normal Quantiles



### Figure 7 

## Quantile plot normalized hands only exposure data with a normal distributio n Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3 -200 -100 0 100 200 300 400Normalized Hands Only Exposure



### Normal Quantiles

### 32 

### Figure 8 

### Quantile plot normalized hands only exposure data with a lognormal distribution Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 4log (Normalized Hands Only Exposure)



### Normal Quantiles



### Figure 9 

### Quantile plot normalized inhalation conc exposure data with a normal distribution Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05Normalized Inhalation Conc Exposure



### Normal Quantiles

### 33 

### Figure 10 

### Quantile plot normalized inhalation conc exposure data with a lognormal distribution Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3 -2.0 -1.5 -1.0 -0.5

0 0.5 1.0 1.5 2.0log (Normalized Inhalation Conc Exposure)



### Normal Quantiles

### 34 

### Figure 11 

### Quantile plot normalized inhalation dose exposure data with a normal distribution Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3 -0.002 -0.001 0 0.001 0.002 0.003 0.004 0.005Normalized Inhalation Dose



### Normal Quantiles



### Figure 12 

### Quantile plot normalized inhalation dose exposure data with a lognormal distribution Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2log (Normalized Inhalation Dose)



### Normal Quantiles

### 35 

### Figure 13

Quantile plot normalized inhalation 8-hour TWA conc exposure data with a normal distribution 

### Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3 -0.0004 -0.0002 0 0.0002 0.0004 0.0006 0.0008Normalized Inhalation 8-hour TWA



### Normal Quantiles



### Figure 14
Quantile plot normalized inhalation 8-hour TWA conc exposure data with a lognormal distribution 

### Normalized by Pounds Active Ingredient Handled

-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2log (Normalized Inhalation 8-hour TWA)



### Normal Quantiles

### 36 

### Log-log-linearity analyses a nd estimated log-log slopes The following analyses evaluate whether the logarithm of exposure is linear in the logarithm of the amount of active ingredient handled (AI) with a slope of 1. We now refer to these analyses as the log-log-linearity analyses. In the Governing Documents and in our statistic al memoranda analyzing previous AEATF studies we have referred to these analyses as a “proportionality” analysis , but this has caused some confusion because the statistical models do not assume that the exposure is directly proportional to the AI but instead assume that the logarithm of the exposure is linear in the logarithm of AI with a slope of 1, which is a related finding but a ve ry different model, as explained here. We have therefore changed the terminology from “proportionality” to “log-log-linearity.” The use of the normalized or unit exposure is based on th e assumption that the exposure is proportional to the normalizing variable pounds of ac tive ingredient handled. Exact proportionality is defined as Exposure = K × Pounds of Active Ingredient, where K is the proportionality constant . Exact proportionality implies that Normalized Exposure = Exposure / Pounds of Active Ingredient = K, so that if the pounds of active ingredie nt is doubled, then the e xposure is exactly doubled, wh ich is not a reasonable assumption due to the variability of exposure for any give n amount of active ingredient. Instead we allow for random multiplicative error terms, which do not depend on the amount of active ingredient, so that Exposure = K × Pounds of Active Ingr edient × Multiplicative Errors, or Normalized Exposure = K × Multiplicative Errors. Since the above quantile plots support th e assumption that the normalized exposur e is log-normally distributed, rather than being normally distributed, we can take natural logarith ms of both sides to get a log- log-linear model of the form Log (Exposure) = Intercept + 1 × Log (Pounds of Active In gredient) + Error Terms. The additive Error Terms are assumed to be normally distri buted with a mean of zero. T hus proportionality of exposure to the pounds of active ingredie nt is statistically modeled by assuming a Slope equal to 1 in the more general log-log linear model: Log (Exposure) = Intercept + Slope × Log (Pounds of Active I ngredient) + Error Terms. Using this general model, taking exponentials of both sides gives
Exposure = e Intercept 

### × (Pounds of Active Ingredient) Slope 

### × e Error Terms 

### , so that Arithmetic Mean Exposure = C × (Pounds of Active Ingredient) Slope 

### , where C = Arithmetic Mean {e Intercept 

### × e Error Terms 

### }. Therefore, the arithmetic mean exposure will be proportional to the pounds of ac tive ingredient if and only if the Slope in the log-log linear mode l equals 1. Note that the proportion ality constant is C, which is very different to the estimated value of Slope. Also note that for this scenario in the mi xed model we assume that the intercept, but not the slope, depends upon which group the source and receiving container belongs to.

### 37 

### Possible alternative models include the same formulation with a Slope of zero, implying that the exposure does not depend upon the amount of active ingredient handled, even though the amount of active ingredient handled varied between the subjects as part of the st udy design. Other possible models include the same model with a slope not equal to zero or one, the quadratic models discussed below, or models with more complicated relationships between the exposure and the experimental conditions. To evaluate whether th e slope is zero, one, or other possible values, we fitted the above statistical model and computed confidence intervals for the slope. To analyze the log-log-linearity, we also considered an add itional hypothetical clothing scenar io with no clothing at all. The dermal exposure for the No clothing scenario was cal culated by summing all the inne r and outer dermal exposure measurements:
All Dermal . This case represents the dermal exposure for a subject wearing no clothes. The e xposure is the sum of the mass from hand wash, face and neck, and the six inner and six outer dosimeters (lower arm, upper arm, lower leg, upper leg, front torso, rear torso).

We can use these statistical models to calculate confiden ce intervals for the slope. The calculation of the confidence intervals depends upon the value of the denominator degrees of freedom for the mixed models used. A review of the alternative methods for calculating the de nominator degrees of freedom for fixe d effects in a mixed model using the SAS MIXED procedure is given in an article by Schaalje et al 1 

### . Based on that article, the following Table 19 summarizes the five available methods: Table 19. SAS Methods for Computing the Fixed Effects Denominator Degrees of Freedom in PROC MIXED.

DDF Method SAS Abbreviation Comments

Residual residual Uses resi dual degrees of freedom. Ignores covariance structure as defined by the RANDOM and REPEATED statements. This method is not recommended.

Containment contain Defa ult method when RANDOM statements are present. Accounts for the minimum contribution of the random effects that syntactically contain the fixed eff ects of interest.

Between-Within bw Default method when REPEATED statements are present and RANDOM statements are not present. Only exact when the data are balanced and the design is a repeated measures design with compound symmetry, and where the levels of the within-subjects effects are not replicated within any of the subjects. Otherwise the method

1 Schaalje, G. B., J. B. McBride, G. W. Fellingham. “Approximations to Distributions of Test Statistics in Complex Mixed Linear M odels Using SAS® Proc MIXED” Proceedings of the Twenty Sixth Annual SAS Users Group International Conference . April 2001. Long Beach, CA. ISBN 1-58025-864-6. SAS Institute, Cary, NC 27513.

### 38 

### DDF Method SAS Abbreviation Comments is at best approximate and can be unpredictable. Satterthwaite / Fai-Cornelius satterth Designed to approximate the denominator degrees of freedom for split-plot designs with complicated covariance structures and/or unbalanced data sets. Kenwood-Rogers kr Designed to approximate the denominator degrees of freedom for designs with complicated covariance structures and/or unbalanced data sets. Results from simulations suggest better performance than the Satterthwaite method. If a covariance parameter has zero variance then this method ignores that covariance.

To interpret this table for this study, note that the RANDOM statement was used to define the worker effect. If the ICC equals zero, then there is no worker clustering and the worker variance equals zero. The REPEATED statement was used to define the repeated measures model. A balanced data set is one where each treatment combination is applied to the same number of subjects. For this st udy, this implies that there are the same number of workers in every group, and each worker has the same number of measured exposure values. The study data were not balanced using the mixed model gr oups Bottle, Conventional, and Reduced Splash, since those groups had 6, 15, and 15 measurements, respectively. Ba sed on this summary, the recommended method is the Kenwood-Rogers method for the mixed models and for the re peated measures model (detailed below). The confidence intervals for the regression coefficients presented in th is memorandum follow these recommendations. Note that this issue does not impact the calcula ted confidence intervals for the summary statis tics in Tables 12 to 18, since they were based on a bootstrap method. Table 20 shows the 95% confidence intervals for the slope calculated from the above lognormal mixed model. Also shown is the width of the confidence interval for the sl ope. A confidence interval that includes one but not zero supports the assumptions of the normaliz ed exposure models. A confidence inte rval that includes zero but not one suggests that the exposure does not de pend on the amount of active ingredient handled. A confidence interval that includes both zero and one suggests that ei ther the basic statistical model is in correct or there are not enough data to statistically infer whether the slope is zero or one. The Repeated Measures statistical model (bottom two rows) is described and discussed below. Note that, because the inha lation dose measured on the OVS tube is mathematically an exact multiple of the corresponding inhalation TWA measured on the OVS tube, the estimated slopes and confidence intervals are exactly the same. As disc ussed above, there were three MEs wher e the measured hands only exposure was unusually high compared to other measurements in the same subgroup (1a, 1b, 2, 3 with CP or with RS) and so the slope estimates for dermal exposures were comput ed with and without th ese potential outliers.

### 39 

### Table 20. 95 percent confidence interval s for the slope of log exposure versus log pounds active ingredient handled. with and without the potential outlier de rmal exposure data for Reduced Splash ME 1 in group 1a, Reduced Splash ME 7 in group 2, and Conventiona l Pour ME 6 in group 1b.

Exposure Route Clothing Data Estimate Lower Upper Confidence Interval Width Dermal (mg) Long pants and long sleeves All 36 Values -0.28 -1.06 0.49 1.5

Exclude outlier data -0.14 -0.84 0.56 1.4 Short pants and short sleeves All 36 Values -0.04 -0.68 0.60 1.3

Exclude outlier data 0.14 -0.50 0.78 1.3 Long pants and short sleeves All 36 Values -0.26 -0.99 0.48 1.5

Exclude outlier data -0.13 -0.78 0.52 1.3 Hands Only All 36 Values -0.31 -1.12 0.50 1.6

Exclude outlier data -0.17 -0.91 0.56 1.5

None All 36 Values -0.05 -0.69 0.59 1.3

Exclude outlier data 0.16 -0.50 0.82 1.3

Inhalation Concentration (mg/m 3 

### ) All 36 Values 1.21 0.71 1.72 1.0

Inhalation Dose (mg) All 36 Values 0.92 0.43 1.42 1.0

Inhalation 8-hour TWA (mg/m 3 

### ) All 36 Values 0.92 0.43 1.42 1.0

Dermal (mg) Repeated Measures Model Any All 36 Values 0.04 -0.61 0.68 1.3

Exclude outlier data 0.14 -0.42 0.71 0.7

For all of the dermal exposure cases, th e confidence interval for the slope incl udes 0 but not 1. Thus, for these cases, the assumption of independence was not re jected and the assumption of log-log-lin earity with slope 1 was rejected. The

### 40 

### estimate slopes are small but sometimes negative, ranging from -0.31 to 0.16. The slopes are higher when the potential outliers are excluded. The negative slope estimates are not expected since one w ould usually assume that the exposure will tend to increase if the amount of ac tive ingredient increases. This may i ndicate some issues with the assumed statistical model, particularly the assu mption that the geometric mean is the same for the three subgroups 1bCP, 2CP and 3CP that are combined into the C onventional group and is the same for th e three subgroups 1bRS, 2RS, 3RS that are combined into the Reduced Splash group. As discussed above, this assumption was need ed so that the same unit exposure estimates could be applied fo r source containers of a ll sizes not pouring into trigger spray bottles.

In the section “Alternative m odels for dermal exposure” we investigate alte rnative models and ou tlier treatments to further understand these negative slopes and in particular to investigate models wh ere the slope is different for the three groups Bottle, Conventional, and Reduced Splash. For all the inhalation exposure cases, the confidence interval for the slope includes 1 but not 0. Thus, for these cases, the assumption of independence was reject ed and the assumption of l og-log-linearity with a slop e of 1 was not rejected and is therefore supported. The slope valu e for the inhalation concentration is a bove 1. As discussed below, when the slope is greater than one, the predicted means from th e normalized exposure model will underestimate the predicted means from the mixed model w ith an estimated slope (of the log exposure against the log amount of active ingredient) when the amount of active ingr edient is high. However, this underestimati on will be small since the slope is only slightly above 1 for the inhalation concen trations, except if the amount of active ingredient ha ndled is extremely high.

The results in Table 20 show that the act ual confidence interval widt hs were mostly less than 1.4 and were at most 1.6 (for hands only). In previous statisti cal analyses of the AEATF studies, an e xpected confidence interval width of at most 1.4 was needed so that the statistical power of detecting log-lo g-linearity would be at least 80%. For this study the statistical design was very different and that power calcul ation does not apply. Neverthele ss, the observed confidence intervals widths in this study are comparable to those found for the m op, wipe, and aerosol studies. The lognormal mixed model regre ssion results are shown in Figures 15 to 22. The scatter plots show the data points in each of the three groups, Bottle, Conventional, and Reduced Splash. The fitted regression lines are shown for each group. The slopes of the regression lines are the same for all three groups (an assumption of the statistical model), but the intercepts are different.

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### Figure 15

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### Figure 16

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### Figure 17

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### Figure 18

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### Figure 19

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### Figure 20

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### Figure 21

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### Figure 22

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### Repeated measures model The above analyses of the log-log-linear ity for dermal exposure show similar sm all slopes. To investigate this issue further, the following more complicated statistical model was fitted to the data of all thre e dermal exposures (excluding the unrealistic hands only and no clothing case) for al l 18 subjects and both Conventional and Reduced Splash containers. The model was of the form: Log (dermal exposure) = LnGM (clothing type and group) + Slope × Log (Pounds of Active Ingredient) + Worker + Error In this model, the intercept depends u pon the clothing type and group, so there are six intercepts. The slope is the same for all three clothing types and both gr oups. The Worker term accounts for possibl e within-worker correlations between their two MEs (i.e. the Conve ntional Pour and Reduced Splash experime nts). Finally, to account for the expected correlations between different dermal exposure measurements on the same worker during th e same ME, the three error terms (one per clothing type) for each worker are assumed to be correlated (with an unspecif ied covariance matrix), but errors for different workers are assumed to be indepe ndent. Thus in SAS terminology, the Worker effect is a RANDOM effect and the Error is a REPE ATED effect where the subject is the combination of the worker and the ME. Thus each worker is treated as two subjects, for their two MEs. We will call this m odel the “Repeated Measures” model. The confidence interval for the slope using this stat istical model are shown in th e bottom two rows of Table 20. Since the confidence interval includes zero and does not incl ude one, the log-log-linearity for dermal exposure has not been shown using this statistical model, but the positive slope estimate suggests that the exposure tends to increase as the AI increases.
Quadratic models The log-log-linearity test was based on a linear model for log exposure versus log pounds active ingredient handled. The HSRB suggested that a quadratic model should also be considered. There are two quadratic models that could be consider ed. Since the original linear model is of the form Log (Exposure) = Intercept + Slope × Log (Pounds of Active Ingredient) + Error Terms, where the intercept depends upon the group but the slope is the same for all three groups, the main quadratic model is of the form Log (Exposure) = Intercept + Slope × Log (Pounds of Active Ingredient) + Quad × {Log (Pounds of Active Ingredient)} 2 

### + Error Terms. The intercept depends upon the group, but the Slope and Quad parameters ar e the same for all three groups. Note that the quadratic term is the square of the logarithm of the pounds of active ingredient rather than the logarithm of the square; the latter approach produces an ill-defined model with two multiples of the logarithm of the pounds of active ingredient. Another approach might be to consid er a quadratic model for exposure:
Exposure = Intercept + Slope × (Pounds of Active Ingredient) + Quad × (Pounds of Active Ingredient) 2 

### + Error Terms.

### 50 

### We do not recommend this second approach for these data since the exposures are known to be non-negative and the quantile plots indicate that the exposure data are better modeled using a log-normal distribution than using a normal distribution. Furthermore, unless the in tercept is zero, this model predicts a nonzero exposure when the pounds of active ingredient is zero , and so a more realistic (though possibly poorer-fitting) model of this form would have a zero intercept for every group. For other e xposure data a log-log-linearity test c ould be carried out by fitting the zero intercept model Exposure = Slope × (Pounds of Active Ingredient) + Quad × (Pounds of Active Ingredient) 2 

### + Error Terms and testing if Quad equals zero. The parsimony principle suggests that the ap propriate statistical procedure for this study is to first fit the quadratic regression model for the l ogarithm of the exposure Log (Exposure) = Intercept + Slope × Log (Pounds of Active Ingredient) + Quad × {Log (Pounds of Active Ingredient)} 2 

### + Error Terms. If the coefficient Quad is statisticall y significant at the 5% level, which is equivalent to requiring that the 95% confidence interval does not include zero, than the quadratic model is supported. Otherwise th e linear model should be used. Table 21 presents the fitted quadratic models from the study for the mixe d models of seven exposure measurements (Long Dermal, Short Dermal, Long Short Dermal, Hands Onl y, and for Inhalation Concentration, Dose and 8-Hour TWA) and for the Repeated Measures model for Dermal e xposures. For the Repeated Measures model, the model has different intercepts (but the same Slope and Quad coefficients) for the six comb inations of group and clothing type. In view of the earlier discussion about de nominator degrees of freedom, the confid ence intervals are calculated using the Kenwood-Rogers method. The group-speci fic intercepts are not shown. Table 21. Quadratic mixed models with 95% confidence in tervals for the log exposure versus log pounds active ingredient handled. Exposure Parameter Estimate Degrees of Freedom Lower Bound Upper Bound GSD ICC Width of Confidence Interval
Long Dermal Slope -3.78 25.64 -9.10 1.54 3.19 0.35 10.64

Long Dermal Quad -0.81 26.37 -2.03 0.41 3.19 0.35 2.44

Short Dermal Slope -1.07 24.69 -5.52 3.37 2.74 0.42 8.89

Short Dermal Quad -0.24 25.42 -1.26 0.78 2.74 0.42 2.05

Long Slope -3.75 25.57 -8.76 1.26 2.99 0.35 10.02

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### Exposure Parameter Estimate Degrees of Freedom Lower Bound Upper Bound GSD ICC Width of Confidence Interval

Short Dermal
Long Short Dermal Quad -0.81 26.29 -1.96 0.34 2.99 0.35 2.30

Hands Only Slope -4.08 25.80 -9.66 1.49 3.35 0.34 11.15

Hands Only Quad -0.88 26.53 -2.15 0.40 3.35 0.34 2.56

Inhalation Conc Slope 0.96 31.00 -2.91 4.82 2.27 0.00 7.74

Inhalation Conc Quad -0.06 31.00 -0.94 0.82 2.27 0.00 1.77

Inhalation Dose Slope 0.25 31.00 -3.52 4.02 2.22 0.00 7.54

Inhalation Dose Quad -0.15 31.00 -1.02 0.71 2.22 0.00 1.72

Inhalation TWA Slope 0.25 31.00 -3.52 4.02 2.22 0.00 7.54

Inhalation TWA Quad -0.15 31.00 -1.02 0.71 2.22 0.00 1.72

Dermal Repeated Measures Slope -0.96 25.10 -5.53 3.61 NA NA -1.91

Dermal Repeated Measures Quad -0.23 25.84 -1.28 0.82 NA NA -0.45

Since the 95% confidence intervals for Qu ad include zero in every case, the quadr atic coefficient is not statistically significant and the quadratic models are not supported. Threshold Analyses

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### As described above, the following two mi xed models were fitted to the de rmal and inhalation exposure data.

Linear mixed model: Log (Exposure) = Intercept1 + Slope × Log (Pounds of Active I ngredient) + Worker + Error Normalized exposure mixed model: Log (Exposure) = Intercept2 + Log (Pounds of Active Ingredient) + Worker + Error,
which is mathematically the same as
Log (Exposure/Pounds of Active Ingredie nt) = Intercept2 + Worker + Error
The intercepts for these two models are de noted as Intercept1 and In tercept2 since their estimated values will in general be different. Intercept1 and Intercept2 both depend upon the group and so each has different values for Bottle, Conventional, and Reduced Splash exposures.
Worker is a normally distributed random effect variable with independent, id entically distributed values for each worker, and Error is a normally distributed error variable with inde pendent, identically distribut ed values for each total exposure measurement. If the linear mixed model has a slope of 1, then the model is mathematically the same as the normalized exposure mixed model.

These two statistical models can be co mpared by calculating the threshold valu e of the pounds of active ingredient at which both models predict the same mean exposure. The threshold values are computed as follows.
Suppose first that the linear mi xed model for log Exposure is correct. Then, as shown above, the predicted arithmetic mean exposure for a given amount of active ingredient is given by the equation Predicted arithmetic mean exposure from linear mixed model = C1 × (Pounds of Active Ingredient) Slope 

### , (1)
where C1 is given by C1 = Arithmetic Mean {e Intercept1 

### × e Error Terms 

### } for the linear mixe d model, so that C1 = exp(Intercept1) × exp( 1⁄2 V1),
where V1 is the total variance for the linear mixed model, calculated as the sum of the worker variance and the error variance. C1 and Intercept1 depends upon the group but V1 is the same for every group. The predicted arithmetic mean exposure is the expected value of the exposure for a given amount of active ingr edient and thus estimates the average (arithmetic mean) exposure for a large num ber of scenarios that ar e all using the same amount of active ingredient. Suppose instead that the normalized exposure mixed model for log Exposure is correct. Then the predicted arithmetic mean exposure is given by the equation Predicted arithmetic mean exposure from normalized exposure mixed model =

### 53 

### C2 × (Pounds of Active Ingredient) 1 

### , (2)
where C2 is given by C2 = Arithmetic Mean {e Intercept2 

### × e Error Terms 

### } for the normalized exposure mixed model, so that C2 = exp(Intercept2) × exp( 1⁄2 V2),

where V2 is the total variance for the normalized exposure mixed model, calculate d as the sum of the worker variance and the error variance. C2 and Intercept2 depend s upon the group but V2 is the same for every group. We now have two estimates of the pr edicted arithmetic mean exposure for a given amount of active ingredient, equations (1) and (2). The graphs in Figures 22 to 43 be low compare the predicted arithmetic means for each clothing configuration (Long Dermal, Short Dermal, Long Short Derm al, Hands Only) and for the three inhalation exposure metrics. There are three plots for each exposure measure corresponding to the three groups, because the threshold value depends upon the group. Exposure is plotted against the pounds of active ingredient. To make it ea sier to see the effects of source container sizes, the da ta points in groups 1, 2, and 3 are labeled by their group number. The green curve gives the predictions for the linear mixed m odel in equation (1). The purple line gi ves the predictions for the normalized exposure mixed model in equation (2). The two estimates (1) and (2) are equal if the pounds of active ingredient equals the Threshold value: Threshold = {C2/C1} 1/(Slope – 1)



### The Threshold values are tabulated in Table 22 below. Suppose that the estimated slope is less than 1. This is true for all the exposure measures studied here except for the inhalation concentration. The predicted arithmetic mean exposure from the normalized exposure mixed model will be greater than the predic ted arithmetic mean exposure from the linear mixed model for amounts of active ingredient above the threshold (right hand side of the graph). The predicted arithmetic mean exposure from the normalized exposure mixed model will be less than the predicted m ean exposure from the linear mixed model for amounts of active ingredient below the thre shold (left hand side of the graph). What th is means is that if we assume log-loglinearity and use the normalized exposure mixed model, then we will tend to over-predict the exposure unless the amount of active ingredient is below th e threshold. (If the amount of active ingredient is be low the threshold, then it will be low enough that the exposure will not usually be of concern).
For the inhalation concentration, the estimated slope was greater than one. In these cases the inequa lities are reversed: The predicted arithmetic mean exposure from the normalized exposure mixed model will be greater than the predicted arithmetic mean exposure from the linear mixed model for amounts of active ingredient be low the threshold (left hand side of the graph). The predicted arithmetic mean expos ure from the normalized exposure mixed model will be less than the predicted arithmetic mean exposure from the lin ear mixed model for amounts of active ingredient above the threshold (right hand side of the grap h). Although these cases show a tenden cy for exposure estimates from the normalized exposure mixed model to under-predict exposure, th e estimated slope is not very much greater than 1 for the inhalation concentration, and then it is clearly seen from the graphs that the two curves are numerically extremely close so that the under-prediction is very small at levels of activ e ingredient similar to t hose used in this study. Table 22. Threshold values for the amount of active ingredient.

Exposure Route Clothing Slope Threshold Level (lb active ingredient) for Bottle Threshold Level (lb active ingredient) for Conventional Threshold Level (lb active ingredient) for Reduced Splash

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### Exposure Route Clothing Slope Threshold Level (lb active ingredient) for Bottle Threshold Level (lb active ingredient) for Conventional Threshold Level (lb active ingredient) for Reduced Splash Dermal (mg) Long pants and long sleeves -0.28 1.14 1.43 0.38

Short pants and short sleeves -0.04 0.83 1.34 0.50

Long pants and short sleeves -0.26 1.07 1.42 0.37

Hands only -0.31 1.19 1.48 0.37

Inhalation Concentration (mg/m 3 

### ) 1.21 0.00025* 0.00271* 0.00073*

Inhalation Dose (mg) 0.92 0.000062 0.00033 0.00015

Inhalation 8-hour TWA (mg/m 3 

### ) 0.92 0.0000078 0.000041 0.000019

*For this case, slope > 1 and so the normalized expos ure mixed model under-predicts exposure for pounds of active ingredient above the threshold.

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### Figure 43 Alternative models for dermal exposure As discussed above, the dermal exposure estimates show so me unexpected patterns, with estimated arithmetic means that are higher for Long Dermal than for Long Short Dermal or higher for Long Short Dermal than for Short Dermal, and with some negative slopes or slopes very close to ze ro. Although the true arithmetic means must increase between Long Dermal, Long Short Dermal and Short Dermal (since the outer dosimeter values for the lower arm and lower leg are added), the estimated arithmetic means from the fitt ed models do not necessary in crease. A negative slope is unexpected since that implies that the e xposure decreases if the amount of active ingredient incr eases, which also seems counter-intuitive. To further investigate these findings we re-fitted the three original models after excluding some outlier values and also investigated alternative m odels for the slopes of the log-log-linear models.

Three alternative sets of outliers were considered:

• No outliers

• Three outliers. These potentia l outliers are for Reduced Splash ME 1 in group 1a, Reduced Splash ME 7 in group 2, and Conventional Pour ME 6 in group 1b. Thes e are three cases where the hands only exposure normalized by the amount of active i ngredient is unusually high compared to other MEs in the same group.

• Four outliers. These potentia l outliers are for Reduced Splash ME 1 in group 1a, Reduced Splash ME 7 in group 2, Conventional Pour ME 6 in group 1b, and Conventiona l Pour ME 10 in group 2. Th e first three are cases

### 76 

### where the hands only exposure normalized by the amount of active ingredient is unusually high compared to other MEs in the same group. The last case is where the hands only exposure is extremely low compared to the other hands only measurements in group 2 but the outer dosimeter for the lower arm is higher than the hands only measurement. Table 23 shows the arithmetic and geometric means of the unit exposure for each clothing scenario and group calculated using the empirical, log-normal simple random sampling, and mixed models af ter excluding these sets of outliers. For each group and data set, the arithmetic and geometric means from the empirical model (AMs and GMs) increase between Long Dermal, Long Short Dermal, and Shor t Dermal. For the lognormal model, the arithmetic mean AMu is estimated as GMs×exp(GSDs) where GSDs is the empirical geometric standard deviation. Although the GMs increases between Long Dermal, Long Short Dermal, and Shor t Dermal, the GSDs and hence the arithmetic mean GMu can decrease. The estimated arithmetic means from the l ognormal model increase as exp ected between Long Dermal, Long Short Dermal, and Short Dermal when the four outlie rs are excluded. For the mixed model it is possible that neither the arithmetic mean AMm nor the geometric mean GMm increase as expected. The estimated geometric means from the lognormal model increase as expected when the three or four outliers are excluded, but the estimated arithmetic means did not consis tently increase as expected. This statistical finding can be regarded as a statistical “ quirk” of the fitted statistical models since the differences between the three dermal unit exposure arithmetic and geomet ric mean estimates are small when compared to their uncertainty (as illustrated in the wide parametric bootstrap confidence interv als displayed in Tables 9, 12, 13, and 14 above). The dermal exposure for this liquid pour scenario is dominated by th e hands only exposure, but the outer dosimeter values for the lower arm a nd lower leg vary considerably. Table 23. Dermal unit exposure (mg/lb AI) arithmetic means and geometric means using alte rnative statistical models and removing zero, three, or four outliers. Clothing Data Group Arithmetic Mean Geometric Mean Empirical Lognormal Mixed Empirical Mixed

AMs AMu AMm GMs GMm Long Dermal No outliers Bottle 155.2511 158.0606 298.4676 116.1970 119.9586 

### Long Short Dermal No outliers Bottle 155.8029 158.5404 280.7180 116.6646 121.5849



### Short Dermal No outliers Bottle 157.7836 160.7434 207.3503 118.5562 108.1348 

### Long Dermal No outliers Conventional 8.3529 10.9082 9.9637 4.1123 4.0046 

### Long Short Dermal No outliers Conventional 8.4623 10.0848 9.9085 4.4159 4.2916



### Short Dermal No outliers Conventional 9.0506 10.7192 9.0011 4.6348 4.6941 

### Long Dermal No outliers Reduced Splash 3.7373 3.6006 3.1400 1.2447 1.2620 

### Long Short Dermal No outliers Reduced Splash 3.7864 3.6543 3.0301 1.2967 1.3124 

### Short Dermal No outliers Reduced Splash 4.2148 3.6551 3.9898 2.0312 2.0807 

### Long Dermal Remove 3 outliers Bottle 94.4075 97.6548 177.5334 88.2638 88.5023

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### Clothing Data Group Arithmetic Mean Geometric Mean Empirical Lognormal Mixed Empirical Mixed

AMs AMu AMm GMs GMm Long Short Dermal Remove 3 outliers Bottle 94.7334 97.9490 166.1035 88.6254 89.0304



### Short Dermal Remove 3 outliers Bottle 96.4299 99.7846 142.2019 90.2199 89.7684 

### Long Dermal Remove 3 outliers Conventional 6.4343 8.3406 7.0752 3.5275 3.5271 

### Long Short Dermal Remove 3 outliers Conventional 6.5494 7.7556 7.1010 3.8070 3.8061



### Short Dermal Remove 3 outliers Conventional 6.8408 8.0949 6.3627 3.9736 4.0166 

### Long Dermal Remove 3 outliers Reduced Splash 1.7623 2.0198 1.9827 0.9884 0.9884 

### Long Short Dermal Remove 3 outliers Reduced Splash 1.8084 2.0722 1.9260 1.0325 1.0323 

### Short Dermal Remove 3 outliers Reduced Splash 2.2127 2.2907 2.6401 1.6672 1.6666 

### Long Dermal Remove 4 outliers Bottle 94.4075 97.6548 159.0276 88.2638 88.2638 

### Long Short Dermal Remove 4 outliers Bottle 94.7334 97.9490 158.5748 88.6254 88.6254



### Short Dermal Remove 4 outliers Bottle 96.4299 99.7846 135.8073 90.2199 90.1188 

### Long Dermal Remove 4 outliers Conventional 6.9103 8.0051 7.7983 4.3282 4.3282 

### Long Short Dermal Remove 4 outliers Conventional 7.0070 8.1406 7.8506 4.3876 4.3876



### Short Dermal Remove 4 outliers Conventional 7.3203 8.4728 6.9460 4.5907 4.6092 

### Long Dermal Remove 4 outliers Reduced Splash 1.7623 2.0198 1.7809 0.9884 0.9884 

### Long Short Dermal Remove 4 outliers Reduced Splash 1.8084 2.0722 1.8475 1.0325 1.0325 

### Short Dermal Remove 4 outliers Reduced Splash 2.2127 2.2907 2.5096 1.6672 1.6653



### The mixed log-log-linear model used to estimate the slopes was of the form: Log (Exposure) = Group Intercept + Slope1 × Log (Pounds of Active Ingredient) + Wo rker1 + Error1 (1) Worker1 is a normally distributed random effect variable with independent, iden tically distributed values for each worker, and Error1 is a normally distri buted error variable with independent, id entically distributed values for each total exposure measurement. The group intercept varies wi th the group. The slope, denoted here as Slope1, and the Worker1 variance, and Error1 variance are each assumed to be the same for each group. Since the mixed model produced negative and small slope es timates for the dermal exposures, we investigated the following alternative models:

### 78 

### Log (Exposure) = Group Intercept + Group Slope2 × Log (P ounds of Active Ingredient) + Worker2 + Error2 (2) Worker2 is a normally distributed random effect variable with independent, iden tically distributed values for each worker, and Error2 is a normally distri buted error variable with independent, id entically distributed values for each total exposure measurement. The group intercept and group sl ope Slope2 each vary with the group. The slope, denoted here as Slope2, and the Worker2 variance, and Error2 va riance are each assumed to be the same for each group. Log (Exposure) = Group Intercept + Group Slope3 × L og (Pounds of Active Ingred ient) + Error3 (3) Error3 is a normally distributed error variable with indepe ndent, identically distributed va lues for each total exposure measurement. The group intercept, group slope Slope3, and Error3 variance each vary with the group.

The difference between models 2 and 3 is that in model 2 the variances of worker and error are assumed to be the same across all there groups, but in model 3 ther e is no worker error and the error vari ances can be different for the different groups. Model 3 is exactly the same as assuming that fo r each group we have the simple linear regression model: Log (Exposure) = Intercept + Slope × L og (Pounds of Active Ingredient) + Error Table 24 shows the estimated slopes and 95% confidence intervals for these three models for each clothing scenario and group after excluding each of the thre e sets of outliers. If no outliers are rem oved, then all the estimated slopes are negative except for a small positive slope for model 3, Short Dermal, in the Reduced Splash group. Compared to model 1, the group-specific slopes in models 2 and 3 have wider confidence intervals and are much more negative for the Bottle group and are more negative for Reduced Splash (e xcept for model 3, Short Dermal). After excluding three or four outliers, the slopes are st ill negative for model 1, but the slopes become positive and very large (about 3) with very wide confidence intervals for Bottle a nd become small (about 0.2) for Conventi onal. After removing three or four outliers, the slopes in models 2 and 3 are about -0.5 and significantly lower than 1 for Reduced Splash Long Dermal and Long Short Dermal. For the Bottle and Conventional groups, after decreasing the amount of data ( by removing outliers) and increasing the number of parameters (by allowing the slope to vary with the group), the conf idence intervals for the slope become wide enough that neither the log-log- linearity with slope 1 as sumption nor the independence assumption can be rejected. For Reduced Splash, the log-log-linearity with slope 1 assumption is rejected and the independence assumption is not rejected in all cases. The finding that these data support independence of exposure and the amount of active ingredient for dermal exposure is likely to be due to the fact that fo r this scenario, the bulk of the dermal exposure occurs due to accidental splashes and spills on the hands. Table 24. Dermal exposure (mg) versus pounds of active ingred ient estimated log-log-linear slopes using alternative statistical models and removing zer o, three, or four outliers. Clothing Data Group Slope1 Slope2 Slope3

Estimate Lower Upper Estimate Lower Upper Estimate Lower Upper
Long Dermal No outliers Bottle -0.28 -1.06 0.49 -2.05 -14.03 9.92 -3.49 -13.47 6.50
Long Short Dermal No outliers Bottle -0.26 -0.99 0.48 -2.04 -13.35 9.28 -3.49 -13.45 6.47

Short Dermal No outliers Bottle -0.04 -0.68 0.60 -3.35 -13.14 6.44 -3.31 -13.37 6.76
Long Dermal No outliers Conventional -0.28 -1.0 6 0.49 -0.09 -1.06 0.89 -0.07 -1.12 0.98
Long Short Dermal No outliers Conventional -0.26 -0.99 0.48 -0.05 -0.97 0.87 -0.04 -0.99 0.91

### 79 

### Clothing Data Group Slope1 Slope2 Slope3

Estimate Lower Upper Estimate Lower Upper Estimate Lower Upper

Short Dermal No outliers Conventional -0.04 -0 .68 0.60 -0.07 -0.87 0.73 -0.04 -1.00 0.91
Long Dermal No outliers Reduced Splash -0.28 -1 .06 0.49 -0.61 -1.84 0.63 -0.57 -1.90 0.76
Long Short Dermal No outliers Reduced Splash -0.2 6 -0.99 0.48 -0.60 -1.77 0.57 -0.57 -1.88 0.74
Short Dermal No outliers Reduced Splash -0.04 -0.68 0.60 -0.03 -1.04 0.97 0.04 -1.03 1.11
Long Dermal Remove 3 outliers Bottle -0.14 -0.8 4 0.56 2.97 -12.27 18.20 2.97 -8.32 14.25
Long Short Dermal Remove 3 outliers Bottle -0.13 -0 .78 0.52 2.95 -11.15 17.05 2.95 -8.28 14.18

Short Dermal Remove 3 outliers Bottle 0.14 -0.5 0 0.78 2.96 -11.02 16.94 3.28 -7.79 14.35
Long Dermal Remove 3 outliers C onventional -0.14 -0.84 0.56 0.16 -0.81 1.12 0.16 -1.09 1.40
Long Short Dermal Remove 3 outlier s Conventional -0.13 -0.78 0.52 0.18 -0.71 1.08 0.18 -0.93 1.30

Short Dermal Remove 3 out liers Conventional 0.14 -0.50 0.78 0.19 -0.70 1.07 0.19 -0.93 1.31
Long Dermal Remove 3 outli ers Reduced Splash -0.14 -0.84 0.56 -0.52 -1.58 0.54 -0.52 -1.48 0.43
Long Short Dermal Remove 3 outliers Reduced Splash -0.13 -0.78 0.52 -0.52 -1.50 0.46 -0.52 -1.45 0.41

Short Dermal Remove 3 out liers Reduced Splash 0.14 -0.50 0.78 0.08 -0.89 1.05 0.08 -0.61 0.78
Long Dermal Remove 4 outliers Bottle -0.10 -0.7 3 0.53 2.97 -10.59 16.52 2.97 -8.32 14.25
Long Short Dermal Remove 4 outliers Bottle -0.10 -0 .72 0.52 2.95 -10.48 16.38 2.95 -8.28 14.18

Short Dermal Remove 4 outliers Bottle 0.18 -0 .42 0.78 3.28 -8.85 15.41 3.28 -7.79 14.35
Long Dermal Remove 4 outliers C onventional -0.10 -0.73 0.53 0.24 -0.62 1.10 0.24 -0.81 1.29
Long Short Dermal Remove 4 outlier s Conventional -0.10 -0.72 0.52 0.24 -0.61 1.09 0.24 -0.81 1.29

Short Dermal Remove 4 out liers Conventional 0.18 -0.42 0.78 0.25 -0.52 1.02 0.25 -0.80 1.30
Long Dermal Remove 4 outli ers Reduced Splash -0.10 -0.73 0.53 -0.52 -1.47 0.42 -0.52 -1.48 0.43
Long Short Dermal Remove 4 outliers Reduced Splash -0.10 -0.72 0.52 -0.52 -1.46 0.41 -0.52 -1.45 0.41

Short Dermal Remove 4 out liers Reduced Splash 0.18 -0.42 0.78 0.08 -0.76 0.93 0.08 -0.61 0.78